arash11/wikipedia-physics-corpus · Datasets at Hugging Face

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By taking into consideration time-varying multistability that is associated with the modulation of large-scale processes (e.g., seasonal forcing) and aggregated feedback of small-scale processes (e.g., convection), the above revised view is refined as follows:	260	Butterfly_effect	https://en.wikipedia.org/wiki/Butterfly_effect	500	40	2,024	8	10	31	0
"The atmosphere possesses chaos and order; it includes, as examples, emerging organized systems (such as tornadoes) and time varying forcing from recurrent seasons."	165	Butterfly_effect	https://en.wikipedia.org/wiki/Butterfly_effect	501	41	2,024	8	10	31	0
The potential for sensitive dependence on initial conditions (the butterfly effect) has been studied in a number of cases in semiclassical and quantum physics, including atoms in strong fields and the anisotropic Kepler problem. Some authors have argued that extreme (exponential) dependence on initial conditions is not expected in pure quantum treatments; however, the sensitive dependence on initial conditions demonstrated in classical motion is included in the semiclassical treatments developed by Martin Gutzwiller and John B. Delos and co-workers. The random matrix theory and simulations with quantum computers prove that some versions of the butterfly effect in quantum mechanics do not exist.	703	Butterfly_effect	https://en.wikipedia.org/wiki/Butterfly_effect	502	42	2,024	8	10	31	0
Other authors suggest that the butterfly effect can be observed in quantum systems. Zbyszek P. Karkuszewski et al. consider the time evolution of quantum systems which have slightly different Hamiltonians. They investigate the level of sensitivity of quantum systems to small changes in their given Hamiltonians. David Poulin et al. presented a quantum algorithm to measure fidelity decay, which "measures the rate at which identical initial states diverge when subjected to slightly different dynamics". They consider fidelity decay to be "the closest quantum analog to the (purely classical) butterfly effect". Whereas the classical butterfly effect considers the effect of a small change in the position and/or velocity of an object in a given Hamiltonian system, the quantum butterfly effect considers the effect of a small change in the Hamiltonian system with a given initial position and velocity. This quantum butterfly effect has been demonstrated experimentally. Quantum and semiclassical treatments of system sensitivity to initial conditions are known as quantum chaos.	1,081	Butterfly_effect	https://en.wikipedia.org/wiki/Butterfly_effect	503	43	2,024	8	10	31	0
The butterfly effect has appeared across mediums such as literature (for instance, A Sound of Thunder), films and television (such as The Simpsons), video games (such as Life Is Strange), AI-driven expansive language models, and more.	234	Butterfly_effect	https://en.wikipedia.org/wiki/Butterfly_effect	504	44	2,024	8	10	31	0
In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution) is a probability distribution or probability measure that gives the probability that a system will be in a certain state as a function of that state's energy and the temperature of the system. The distribution is expressed in the form:	335	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	505	0	2,024	8	10	31	0
where p i is the probability of the system being in state i, exp is the exponential function, ε i is the energy of that state, and a constant kT of the distribution is the product of the Boltzmann constant k and thermodynamic temperature T. The symbol ∝ ∝ denotes proportionality (see § The distribution for the proportionality constant).	338	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	506	1	2,024	8	10	31	0
The term system here has a wide meaning; it can range from a collection of 'sufficient number' of atoms or a single atom to a macroscopic system such as a natural gas storage tank. Therefore the Boltzmann distribution can be used to solve a wide variety of problems. The distribution shows that states with lower energy will always have a higher probability of being occupied.	376	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	507	2	2,024	8	10	31	0
The ratio of probabilities of two states is known as the Boltzmann factor and characteristically only depends on the states' energy difference:	143	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	508	3	2,024	8	10	31	0
The Boltzmann distribution is named after Ludwig Boltzmann who first formulated it in 1868 during his studies of the statistical mechanics of gases in thermal equilibrium. Boltzmann's statistical work is borne out in his paper “On the Relationship between the Second Fundamental Theorem of the Mechanical Theory of Heat and Probability Calculations Regarding the Conditions for Thermal Equilibrium" The distribution was later investigated extensively, in its modern generic form, by Josiah Willard Gibbs in 1902.	512	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	509	4	2,024	8	10	31	0
The Boltzmann distribution should not be confused with the Maxwell–Boltzmann distribution or Maxwell-Boltzmann statistics. The Boltzmann distribution gives the probability that a system will be in a certain state as a function of that state's energy, while the Maxwell-Boltzmann distributions give the probabilities of particle speeds or energies in ideal gases. The distribution of energies in a one-dimensional gas however, does follow the Boltzmann distribution.	465	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	510	5	2,024	8	10	31	0
The Boltzmann distribution is a probability distribution that gives the probability of a certain state as a function of that state's energy and temperature of the system to which the distribution is applied. It is given as p i = 1 Q exp ⁡ ⁡ ( − − ε ε i k T ) = exp ⁡ ⁡ ( − − ε ε i k T ) ∑ ∑ j = 1 M exp ⁡ ⁡ ( − − ε ε j k T )	324	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	511	6	2,024	8	10	31	0
where:	6	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	512	7	2,024	8	10	31	0
Using Lagrange multipliers, one can prove that the Boltzmann distribution is the distribution that maximizes the entropy S ( p 1 , p 2 , ⋯ ⋯ , p M ) = − − ∑ ∑ i = 1 M p i log 2 ⁡ ⁡ p i	184	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	513	8	2,024	8	10	31	0
subject to the normalization constraint that ∑ ∑ p i = 1 and the constraint that ∑ ∑ p i ε ε i equals a particular mean energy value, except for two special cases. (These special cases occur when the mean value is either the minimum or maximum of the energies ε i. In these cases, the entropy maximizing distribution is a limit of Boltzmann distributions where T approaches zero from above or below, respectively.)	414	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	514	9	2,024	8	10	31	0
The partition function can be calculated if we know the energies of the states accessible to the system of interest. For atoms the partition function values can be found in the NIST Atomic Spectra Database.	206	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	515	10	2,024	8	10	31	0
The distribution shows that states with lower energy will always have a higher probability of being occupied than the states with higher energy. It can also give us the quantitative relationship between the probabilities of the two states being occupied. The ratio of probabilities for states i and j is given as p i p j = exp ⁡ ⁡ ( ε ε j − − ε ε i k T )	354	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	516	11	2,024	8	10	31	0
where:	6	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	517	12	2,024	8	10	31	0
The corresponding ratio of populations of energy levels must also take their degeneracies into account.	103	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	518	13	2,024	8	10	31	0
The Boltzmann distribution is often used to describe the distribution of particles, such as atoms or molecules, over bound states accessible to them. If we have a system consisting of many particles, the probability of a particle being in state i is practically the probability that, if we pick a random particle from that system and check what state it is in, we will find it is in state i. This probability is equal to the number of particles in state i divided by the total number of particles in the system, that is the fraction of particles that occupy state i.	566	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	519	14	2,024	8	10	31	0
where N i is the number of particles in state i and N is the total number of particles in the system. We may use the Boltzmann distribution to find this probability that is, as we have seen, equal to the fraction of particles that are in state i. So the equation that gives the fraction of particles in state i as a function of the energy of that state is N i N = exp ⁡ ⁡ ( − − ε ε i k T ) ∑ ∑ j = 1 M exp ⁡ ⁡ ( − − ε ε j k T )	427	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	520	15	2,024	8	10	31	0
This equation is of great importance to spectroscopy. In spectroscopy we observe a spectral line of atoms or molecules undergoing transitions from one state to another. In order for this to be possible, there must be some particles in the first state to undergo the transition. We may find that this condition is fulfilled by finding the fraction of particles in the first state. If it is negligible, the transition is very likely not observed at the temperature for which the calculation was done. In general, a larger fraction of molecules in the first state means a higher number of transitions to the second state. This gives a stronger spectral line. However, there are other factors that influence the intensity of a spectral line, such as whether it is caused by an allowed or a forbidden transition.	807	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	521	16	2,024	8	10	31	0
The softmax function commonly used in machine learning is related to the Boltzmann distribution:	96	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	522	17	2,024	8	10	31	0
Distribution of the form	24	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	523	18	2,024	8	10	31	0
is called generalized Boltzmann distribution by some authors.	61	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	524	19	2,024	8	10	31	0
The Boltzmann distribution is a special case of the generalized Boltzmann distribution. The generalized Boltzmann distribution is used in statistical mechanics to describe canonical ensemble, grand canonical ensemble and isothermal–isobaric ensemble. The generalized Boltzmann distribution is usually derived from the principle of maximum entropy, but there are other derivations.	380	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	525	20	2,024	8	10	31	0
The generalized Boltzmann distribution has the following properties:	68	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	526	21	2,024	8	10	31	0
The Boltzmann distribution appears in statistical mechanics when considering closed systems of fixed composition that are in thermal equilibrium (equilibrium with respect to energy exchange). The most general case is the probability distribution for the canonical ensemble. Some special cases (derivable from the canonical ensemble) show the Boltzmann distribution in different aspects:	386	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	527	22	2,024	8	10	31	0
Although these cases have strong similarities, it is helpful to distinguish them as they generalize in different ways when the crucial assumptions are changed:	159	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	528	23	2,024	8	10	31	0
The Boltzmann distribution can be introduced to allocate permits in emissions trading. The new allocation method using the Boltzmann distribution can describe the most probable, natural, and unbiased distribution of emissions permits among multiple countries.	259	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	529	24	2,024	8	10	31	0
The Boltzmann distribution has the same form as the multinomial logit model. As a discrete choice model, this is very well known in economics since Daniel McFadden made the connection to random utility maximization.	215	Boltzmann_distribution	https://en.wikipedia.org/wiki/Boltzmann_distribution	530	25	2,024	8	10	31	0
The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. It was first proposed as a physical theory in 1931 by Roman Catholic priest and physicist Georges Lemaître when he suggested the universe emerged from a "primeval atom". Various cosmological models of the Big Bang explain the evolution of the observable universe from the earliest known periods through its subsequent large-scale form. These models offer a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure. The uniformity of the universe, known as the flatness problem, is explained through cosmic inflation : a sudden and very rapid expansion of space during the earliest moments.	847	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	531	0	2,024	8	10	31	0
Crucially, these models are compatible with the Hubble–Lemaître law —the observation that the farther away a galaxy is, the faster it is moving away from Earth. Extrapolating this cosmic expansion backward in time using the known laws of physics, the models describe an increasingly concentrated cosmos preceded by a singularity in which space and time lose meaning (typically named "the Big Bang singularity"). Physics lacks a widely accepted theory of quantum gravity that can model the earliest conditions of the Big Bang. In 1964 the CMB was discovered, which convinced many cosmologists that the competing steady-state model of cosmic evolution was falsified, since the Big Bang models predict a uniform background radiation caused by high temperatures and densities in the distant past. A wide range of empirical evidence strongly favors the Big Bang event, which is now essentially universally accepted. Detailed measurements of the expansion rate of the universe place the Big Bang singularity at an estimated 13.787 ± 0.020 billion years ago, which is considered the age of the universe.	1,096	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	532	1	2,024	8	10	31	0
There remain aspects of the observed universe that are not yet adequately explained by the Big Bang models. After its initial expansion, the universe cooled sufficiently to allow the formation of subatomic particles, and later atoms. The unequal abundances of matter and antimatter that allowed this to occur is an unexplained effect known as baryon asymmetry. These primordial elements—mostly hydrogen, with some helium and lithium —later coalesced through gravity, forming early stars and galaxies. Astronomers observe the gravitational effects of an unknown dark matter surrounding galaxies. Most of the gravitational potential in the universe seems to be in this form, and the Big Bang models and various observations indicate that this excess gravitational potential is not created by baryonic matter, such as normal atoms. Measurements of the redshifts of supernovae indicate that the expansion of the universe is accelerating, an observation attributed to an unexplained phenomenon known as dark energy.	1,010	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	533	2	2,024	8	10	31	0
The Big Bang models offer a comprehensive explanation for a broad range of observed phenomena, including the abundances of the light elements, the CMB, large-scale structure, and Hubble's law. The models depend on two major assumptions: the universality of physical laws and the cosmological principle. The universality of physical laws is one of the underlying principles of the theory of relativity. The cosmological principle states that on large scales the universe is homogeneous and isotropic —appearing the same in all directions regardless of location.	560	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	534	3	2,024	8	10	31	0
These ideas were initially taken as postulates, but later efforts were made to test each of them. For example, the first assumption has been tested by observations showing that the largest possible deviation of the fine-structure constant over much of the age of the universe is of order 10. Also, general relativity has passed stringent tests on the scale of the Solar System and binary stars.	394	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	535	4	2,024	8	10	31	0
The large-scale universe appears isotropic as viewed from Earth. If it is indeed isotropic, the cosmological principle can be derived from the simpler Copernican principle, which states that there is no preferred (or special) observer or vantage point. To this end, the cosmological principle has been confirmed to a level of 10 via observations of the temperature of the CMB. At the scale of the CMB horizon, the universe has been measured to be homogeneous with an upper bound on the order of 10% inhomogeneity, as of 1995.	525	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	536	5	2,024	8	10	31	0
An important feature of the Big Bang spacetime is the presence of particle horizons. Since the universe has a finite age, and light travels at a finite speed, there may be events in the past whose light has not yet had time to reach earth. This places a limit or a past horizon on the most distant objects that can be observed. Conversely, because space is expanding, and more distant objects are receding ever more quickly, light emitted by us today may never "catch up" to very distant objects. This defines a future horizon, which limits the events in the future that we will be able to influence. The presence of either type of horizon depends on the details of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric that describes the expansion of the universe.	765	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	537	6	2,024	8	10	31	0
Our understanding of the universe back to very early times suggests that there is a past horizon, though in practice our view is also limited by the opacity of the universe at early times. So our view cannot extend further backward in time, though the horizon recedes in space. If the expansion of the universe continues to accelerate, there is a future horizon as well.	370	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	538	7	2,024	8	10	31	0
Some processes in the early universe occurred too slowly, compared to the expansion rate of the universe, to reach approximate thermodynamic equilibrium. Others were fast enough to reach thermalization. The parameter usually used to find out whether a process in the very early universe has reached thermal equilibrium is the ratio between the rate of the process (usually rate of collisions between particles) and the Hubble parameter. The larger the ratio, the more time particles had to thermalize before they were too far away from each other.	547	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	539	8	2,024	8	10	31	0
According to the Big Bang models, the universe at the beginning was very hot and very compact, and since then it has been expanding and cooling.	144	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	540	9	2,024	8	10	31	0
In the absence of a perfect cosmological principle, extrapolation of the expansion of the universe backwards in time using general relativity yields an infinite density and temperature at a finite time in the past. This irregular behavior, known as the gravitational singularity, indicates that general relativity is not an adequate description of the laws of physics in this regime. Models based on general relativity alone cannot fully extrapolate toward the singularity. In some proposals, such as the emergent Universe models, the singularity is replaced by another cosmological epoch. A different approach identifies the initial singularity as a singularity predicted by some models of the Big Bang theory to have existed before the Big Bang event.	753	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	541	10	2,024	8	10	31	0
This primordial singularity is itself sometimes called "the Big Bang", but the term can also refer to a more generic early hot, dense phase of the universe. In either case, "the Big Bang" as an event is also colloquially referred to as the "birth" of our universe since it represents the point in history where the universe can be verified to have entered into a regime where the laws of physics as we understand them (specifically general relativity and the Standard Model of particle physics) work. Based on measurements of the expansion using Type Ia supernovae and measurements of temperature fluctuations in the cosmic microwave background, the time that has passed since that event—known as the " age of the universe "—is 13.8 billion years.	747	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	542	11	2,024	8	10	31	0
Despite being extremely dense at this time—far denser than is usually required to form a black hole —the universe did not re-collapse into a singularity. Commonly used calculations and limits for explaining gravitational collapse are usually based upon objects of relatively constant size, such as stars, and do not apply to rapidly expanding space such as the Big Bang. Since the early universe did not immediately collapse into a multitude of black holes, matter at that time must have been very evenly distributed with a negligible density gradient.	552	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	543	12	2,024	8	10	31	0
The earliest phases of the Big Bang are subject to much speculation, given the lack of available data. In the most common models the universe was filled homogeneously and isotropically with a very high energy density and huge temperatures and pressures, and was very rapidly expanding and cooling. The period up to 10 seconds into the expansion, the Planck epoch, was a phase in which the four fundamental forces —the electromagnetic force, the strong nuclear force, the weak nuclear force, and the gravitational force, were unified as one. In this stage, the characteristic scale length of the universe was the Planck length, 1.6 × 10 m, and consequently had a temperature of approximately 10 degrees Celsius. Even the very concept of a particle breaks down in these conditions. A proper understanding of this period awaits the development of a theory of quantum gravity. The Planck epoch was succeeded by the grand unification epoch beginning at 10 seconds, where gravitation separated from the other forces as the universe's temperature fell.	1,045	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	544	13	2,024	8	10	31	3	EPOCH, UNITS, EPOCH
At approximately 10 seconds into the expansion, a phase transition caused a cosmic inflation, during which the universe grew exponentially, unconstrained by the light speed invariance, and temperatures dropped by a factor of 100,000. This concept is motivated by the flatness problem, where the density of matter and energy is very close to the critical density needed to produce a flat universe. That is, the shape of the universe has no overall geometric curvature due to gravitational influence. Microscopic quantum fluctuations that occurred because of Heisenberg's uncertainty principle were "frozen in" by inflation, becoming amplified into the seeds that would later form the large-scale structure of the universe. At a time around 10 seconds, the electroweak epoch begins when the strong nuclear force separates from the other forces, with only the electromagnetic force and weak nuclear force remaining unified.	920	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	545	14	2,024	8	10	31	0
Inflation stopped locally at around 10 to 10 seconds, with the observable universe's volume having increased by a factor of at least 10. Reheating followed as the inflaton field decayed, until the universe obtained the temperatures required for the production of a quark–gluon plasma as well as all other elementary particles. Temperatures were so high that the random motions of particles were at relativistic speeds, and particle–antiparticle pairs of all kinds were being continuously created and destroyed in collisions. At some point, an unknown reaction called baryogenesis violated the conservation of baryon number, leading to a very small excess of quarks and leptons over antiquarks and antileptons—of the order of one part in 30 million. This resulted in the predominance of matter over antimatter in the present universe.	833	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	546	15	2,024	8	10	31	0
The universe continued to decrease in density and fall in temperature, hence the typical energy of each particle was decreasing. Symmetry-breaking phase transitions put the fundamental forces of physics and the parameters of elementary particles into their present form, with the electromagnetic force and weak nuclear force separating at about 10 seconds.	356	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	547	16	2,024	8	10	31	0
After about 10 seconds, the picture becomes less speculative, since particle energies drop to values that can be attained in particle accelerators. At about 10 seconds, quarks and gluons combined to form baryons such as protons and neutrons. The small excess of quarks over antiquarks led to a small excess of baryons over antibaryons. The temperature was no longer high enough to create either new proton–antiproton or neutron–antineutron pairs. A mass annihilation immediately followed, leaving just one in 10 of the original matter particles and none of their antiparticles. A similar process happened at about 1 second for electrons and positrons. After these annihilations, the remaining protons, neutrons and electrons were no longer moving relativistically and the energy density of the universe was dominated by photons (with a minor contribution from neutrinos).	871	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	548	17	2,024	8	10	31	0
A few minutes into the expansion, when the temperature was about a billion kelvin and the density of matter in the universe was comparable to the current density of Earth's atmosphere, neutrons combined with protons to form the universe's deuterium and helium nuclei in a process called Big Bang nucleosynthesis (BBN). Most protons remained uncombined as hydrogen nuclei.	371	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	549	18	2,024	8	10	31	0
As the universe cooled, the rest energy density of matter came to gravitationally dominate that of the photon radiation. The recombination epoch began after about 379,000 years, when the electrons and nuclei combined into atoms (mostly hydrogen), which were able to emit radiation. This relic radiation, which continued through space largely unimpeded, is known as the cosmic microwave background.	397	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	550	19	2,024	8	10	31	0
After the recombination epoch, the slightly denser regions of the uniformly distributed matter gravitationally attracted nearby matter and thus grew even denser, forming gas clouds, stars, galaxies, and the other astronomical structures observable today. The details of this process depend on the amount and type of matter in the universe. The four possible types of matter are known as cold dark matter (CDM), warm dark matter, hot dark matter, and baryonic matter. The best measurements available, from the Wilkinson Microwave Anisotropy Probe (WMAP), show that the data is well-fit by a Lambda-CDM model in which dark matter is assumed to be cold. (Warm dark matter is ruled out by early reionization.) This CDM is estimated to make up about 23% of the matter/energy of the universe, while baryonic matter makes up about 4.6%.	829	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	551	20	2,024	8	10	31	0
In an "extended model" which includes hot dark matter in the form of neutrinos, then the "physical baryon density" Ω Ω b h 2 is estimated at 0.023. (This is different from the 'baryon density' Ω Ω b expressed as a fraction of the total matter/energy density, which is about 0.046.) The corresponding cold dark matter density Ω Ω c h 2 is about 0.11, and the corresponding neutrino density Ω Ω v h 2 is estimated to be less than 0.0062.	435	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	552	21	2,024	8	10	31	0
Independent lines of evidence from Type Ia supernovae and the CMB imply that the universe today is dominated by a mysterious form of energy known as dark energy, which appears to homogeneously permeate all of space. Observations suggest that 73% of the total energy density of the present day universe is in this form. When the universe was very young it was likely infused with dark energy, but with everything closer together, gravity predominated, braking the expansion. Eventually, after billions of years of expansion, the declining density of matter relative to the density of dark energy allowed the expansion of the universe to begin to accelerate.	656	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	553	22	2,024	8	10	31	0
Dark energy in its simplest formulation is modeled by a cosmological constant term in Einstein field equations of general relativity, but its composition and mechanism are unknown. More generally, the details of its equation of state and relationship with the Standard Model of particle physics continue to be investigated both through observation and theory.	359	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	554	23	2,024	8	10	31	0
All of this cosmic evolution after the inflationary epoch can be rigorously described and modeled by the lambda-CDM model of cosmology, which uses the independent frameworks of quantum mechanics and general relativity. There are no easily testable models that would describe the situation prior to approximately 10 seconds. Understanding this earliest of eras in the history of the universe is one of the greatest unsolved problems in physics.	443	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	555	24	2,024	8	10	31	0
English astronomer Fred Hoyle is credited with coining the term "Big Bang" during a talk for a March 1949 BBC Radio broadcast, saying: "These theories were based on the hypothesis that all the matter in the universe was created in one big bang at a particular time in the remote past." However, it did not catch on until the 1970s.	331	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	556	25	2,024	8	10	31	0
It is popularly reported that Hoyle, who favored an alternative " steady-state " cosmological model, intended this to be pejorative, but Hoyle explicitly denied this and said it was just a striking image meant to highlight the difference between the two models. Helge Kragh writes that the evidence for the claim that it was meant as a pejorative is "unconvincing", and mentions a number of indications that it was not a pejorative.	432	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	557	26	2,024	8	10	31	0
The term itself has been argued to be a misnomer because it evokes an explosion. The argument is that whereas an explosion suggests expansion into a surrounding space, the Big Bang only describes the intrinsic expansion of the contents of the universe. Another issue pointed out by Santhosh Mathew is that bang implies sound, which is not an important feature of the model. An attempt to find a more suitable alternative was not successful.	440	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	558	27	2,024	8	10	31	0
The Big Bang models developed from observations of the structure of the universe and from theoretical considerations. In 1912, Vesto Slipher measured the first Doppler shift of a " spiral nebula " (spiral nebula is the obsolete term for spiral galaxies), and soon discovered that almost all such nebulae were receding from Earth. He did not grasp the cosmological implications of this fact, and indeed at the time it was highly controversial whether or not these nebulae were "island universes" outside our Milky Way. Ten years later, Alexander Friedmann, a Russian cosmologist and mathematician, derived the Friedmann equations from the Einstein field equations, showing that the universe might be expanding in contrast to the static universe model advocated by Albert Einstein at that time.	792	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	559	28	2,024	8	10	31	0
In 1924, American astronomer Edwin Hubble 's measurement of the great distance to the nearest spiral nebulae showed that these systems were indeed other galaxies. Starting that same year, Hubble painstakingly developed a series of distance indicators, the forerunner of the cosmic distance ladder, using the 100-inch (2.5 m) Hooker telescope at Mount Wilson Observatory. This allowed him to estimate distances to galaxies whose redshifts had already been measured, mostly by Slipher. In 1929, Hubble discovered a correlation between distance and recessional velocity —now known as Hubble's law.	594	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	560	29	2,024	8	10	31	0
Independently deriving Friedmann's equations in 1927, Georges Lemaître, a Belgian physicist and Roman Catholic priest, proposed that the recession of the nebulae was due to the expansion of the universe. He inferred the relation that Hubble would later observe, given the cosmological principle. In 1931, Lemaître went further and suggested that the evident expansion of the universe, if projected back in time, meant that the further in the past the smaller the universe was, until at some finite time in the past all the mass of the universe was concentrated into a single point, a "primeval atom" where and when the fabric of time and space came into existence.	664	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	561	30	2,024	8	10	31	0
In the 1920s and 1930s, almost every major cosmologist preferred an eternal steady-state universe, and several complained that the beginning of time implied by the Big Bang imported religious concepts into physics; this objection was later repeated by supporters of the steady-state theory. This perception was enhanced by the fact that the originator of the Big Bang concept, Lemaître, was a Roman Catholic priest. Arthur Eddington agreed with Aristotle that the universe did not have a beginning in time, viz., that matter is eternal. A beginning in time was "repugnant" to him. Lemaître, however, disagreed:	610	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	562	31	2,024	8	10	31	0
If the world has begun with a single quantum, the notions of space and time would altogether fail to have any meaning at the beginning; they would only begin to have a sensible meaning when the original quantum had been divided into a sufficient number of quanta. If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time.	379	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	563	32	2,024	8	10	31	0
During the 1930s, other ideas were proposed as non-standard cosmologies to explain Hubble's observations, including the Milne model, the oscillatory universe (originally suggested by Friedmann, but advocated by Albert Einstein and Richard C. Tolman) and Fritz Zwicky 's tired light hypothesis.	293	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	564	33	2,024	8	10	31	0
After World War II, two distinct possibilities emerged. One was Fred Hoyle's steady-state model, whereby new matter would be created as the universe seemed to expand. In this model the universe is roughly the same at any point in time. The other was Lemaître's Big Bang theory, advocated and developed by George Gamow, who introduced BBN and whose associates, Ralph Alpher and Robert Herman, predicted the CMB. Ironically, it was Hoyle who coined the phrase that came to be applied to Lemaître's theory, referring to it as "this big bang idea" during a BBC Radio broadcast in March 1949. For a while, support was split between these two theories. Eventually, the observational evidence, most notably from radio source counts, began to favor Big Bang over steady state. The discovery and confirmation of the CMB in 1964 secured the Big Bang as the best theory of the origin and evolution of the universe.	903	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	565	34	2,024	8	10	31	0
In 1968 and 1970, Roger Penrose, Stephen Hawking, and George F. R. Ellis published papers where they showed that mathematical singularities were an inevitable initial condition of relativistic models of the Big Bang. Then, from the 1970s to the 1990s, cosmologists worked on characterizing the features of the Big Bang universe and resolving outstanding problems. In 1981, Alan Guth made a breakthrough in theoretical work on resolving certain outstanding theoretical problems in the Big Bang models with the introduction of an epoch of rapid expansion in the early universe he called "inflation". Meanwhile, during these decades, two questions in observational cosmology that generated much discussion and disagreement were over the precise values of the Hubble Constant and the matter-density of the universe (before the discovery of dark energy, thought to be the key predictor for the eventual fate of the universe).	920	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	566	35	2,024	8	10	31	0
In the mid-1990s, observations of certain globular clusters appeared to indicate that they were about 15 billion years old, which conflicted with most then-current estimates of the age of the universe (and indeed with the age measured today). This issue was later resolved when new computer simulations, which included the effects of mass loss due to stellar winds, indicated a much younger age for globular clusters.	417	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	567	36	2,024	8	10	31	0
Significant progress in Big Bang cosmology has been made since the late 1990s as a result of advances in telescope technology as well as the analysis of data from satellites such as the Cosmic Background Explorer (COBE), the Hubble Space Telescope and WMAP. Cosmologists now have fairly precise and accurate measurements of many of the parameters of the Big Bang model, and have made the unexpected discovery that the expansion of the universe appears to be accelerating.	471	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	568	37	2,024	8	10	31	0
"[The] big bang picture is too firmly grounded in data from every area to be proved invalid in its general features."	117	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	569	38	2,024	8	10	31	0
— Lawrence Krauss	17	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	570	39	2,024	8	10	31	0
The earliest and most direct observational evidence of the validity of the theory are the expansion of the universe according to Hubble's law (as indicated by the redshifts of galaxies), discovery and measurement of the cosmic microwave background and the relative abundances of light elements produced by Big Bang nucleosynthesis (BBN). More recent evidence includes observations of galaxy formation and evolution, and the distribution of large-scale cosmic structures, These are sometimes called the "four pillars" of the Big Bang models.	540	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	571	40	2,024	8	10	31	0
Precise modern models of the Big Bang appeal to various exotic physical phenomena that have not been observed in terrestrial laboratory experiments or incorporated into the Standard Model of particle physics. Of these features, dark matter is currently the subject of most active laboratory investigations. Remaining issues include the cuspy halo problem and the dwarf galaxy problem of cold dark matter. Dark energy is also an area of intense interest for scientists, but it is not clear whether direct detection of dark energy will be possible. Inflation and baryogenesis remain more speculative features of current Big Bang models. Viable, quantitative explanations for such phenomena are still being sought. These are unsolved problems in physics.	751	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	572	41	2,024	8	10	31	0
Observations of distant galaxies and quasars show that these objects are redshifted: the light emitted from them has been shifted to longer wavelengths. This can be seen by taking a frequency spectrum of an object and matching the spectroscopic pattern of emission or absorption lines corresponding to atoms of the chemical elements interacting with the light. These redshifts are uniformly isotropic, distributed evenly among the observed objects in all directions. If the redshift is interpreted as a Doppler shift, the recessional velocity of the object can be calculated. For some galaxies, it is possible to estimate distances via the cosmic distance ladder. When the recessional velocities are plotted against these distances, a linear relationship known as Hubble's law is observed: v = H 0 D where	805	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	573	42	2,024	8	10	31	0
Hubble's law implies that the universe is uniformly expanding everywhere. This cosmic expansion was predicted from general relativity by Friedmann in 1922 and Lemaître in 1927, well before Hubble made his 1929 analysis and observations, and it remains the cornerstone of the Big Bang model as developed by Friedmann, Lemaître, Robertson, and Walker.	349	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	574	43	2,024	8	10	31	0
The theory requires the relation v = H D to hold at all times, where D is the proper distance, v is the recessional velocity, and v , H , and D vary as the universe expands (hence we write H 0 to denote the present-day Hubble "constant"). For distances much smaller than the size of the observable universe, the Hubble redshift can be thought of as the Doppler shift corresponding to the recession velocity v . For distances comparable to the size of the observable universe, the attribution of the cosmological redshift becomes more ambiguous, although its interpretation as a kinematic Doppler shift remains the most natural one.	631	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	575	44	2,024	8	10	31	0
An unexplained discrepancy with the determination of the Hubble constant is known as Hubble tension. Techniques based on observation of the CMB suggest a lower value of this constant compared to the quantity derived from measurements based on the cosmic distance ladder.	270	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	576	45	2,024	8	10	31	0
In 1964, Arno Penzias and Robert Wilson serendipitously discovered the cosmic background radiation, an omnidirectional signal in the microwave band. Their discovery provided substantial confirmation of the big-bang predictions by Alpher, Herman and Gamow around 1950. Through the 1970s, the radiation was found to be approximately consistent with a blackbody spectrum in all directions; this spectrum has been redshifted by the expansion of the universe, and today corresponds to approximately 2.725 K. This tipped the balance of evidence in favor of the Big Bang model, and Penzias and Wilson were awarded the 1978 Nobel Prize in Physics.	639	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	577	46	2,024	8	10	31	0
The surface of last scattering corresponding to emission of the CMB occurs shortly after recombination, the epoch when neutral hydrogen becomes stable. Prior to this, the universe comprised a hot dense photon-baryon plasma sea where photons were quickly scattered from free charged particles. Peaking at around 372 ± 14 kyr, the mean free path for a photon becomes long enough to reach the present day and the universe becomes transparent.	439	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	578	47	2,024	8	10	31	0
In 1989, NASA launched COBE, which made two major advances: in 1990, high-precision spectrum measurements showed that the CMB frequency spectrum is an almost perfect blackbody with no deviations at a level of 1 part in 10, and measured a residual temperature of 2.726 K (more recent measurements have revised this figure down slightly to 2.7255 K); then in 1992, further COBE measurements discovered tiny fluctuations (anisotropies) in the CMB temperature across the sky, at a level of about one part in 10. John C. Mather and George Smoot were awarded the 2006 Nobel Prize in Physics for their leadership in these results.	623	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	579	48	2,024	8	10	31	0
During the following decade, CMB anisotropies were further investigated by a large number of ground-based and balloon experiments. In 2000–2001, several experiments, most notably BOOMERanG, found the shape of the universe to be spatially almost flat by measuring the typical angular size (the size on the sky) of the anisotropies.	330	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	580	49	2,024	8	10	31	0
In early 2003, the first results of the Wilkinson Microwave Anisotropy Probe were released, yielding what were at the time the most accurate values for some of the cosmological parameters. The results disproved several specific cosmic inflation models, but are consistent with the inflation theory in general. The Planck space probe was launched in May 2009. Other ground and balloon-based cosmic microwave background experiments are ongoing.	442	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	581	50	2,024	8	10	31	1	MISSION
Using Big Bang models, it is possible to calculate the expected concentration of the isotopes helium-4 (He), helium-3 (He), deuterium (H), and lithium-7 (Li) in the universe as ratios to the amount of ordinary hydrogen. The relative abundances depend on a single parameter, the ratio of photons to baryons. This value can be calculated independently from the detailed structure of CMB fluctuations. The ratios predicted (by mass, not by abundance) are about 0.25 for He:H, about 10 for H:H, about 10 for He:H, and about 10 for Li:H.	532	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	582	51	2,024	8	10	31	0
The measured abundances all agree at least roughly with those predicted from a single value of the baryon-to-photon ratio. The agreement is excellent for deuterium, close but formally discrepant for He, and off by a factor of two for Li (this anomaly is known as the cosmological lithium problem); in the latter two cases, there are substantial systematic uncertainties. Nonetheless, the general consistency with abundances predicted by BBN is strong evidence for the Big Bang, as the theory is the only known explanation for the relative abundances of light elements, and it is virtually impossible to "tune" the Big Bang to produce much more or less than 20–30% helium. Indeed, there is no obvious reason outside of the Big Bang that, for example, the young universe before star formation, as determined by studying matter supposedly free of stellar nucleosynthesis products, should have more helium than deuterium or more deuterium than He, and in constant ratios, too.	972	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	583	52	2,024	8	10	31	0
Detailed observations of the morphology and distribution of galaxies and quasars are in agreement with the current Big Bang models. A combination of observations and theory suggest that the first quasars and galaxies formed within a billion years after the Big Bang, and since then, larger structures have been forming, such as galaxy clusters and superclusters.	362	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	584	53	2,024	8	10	31	0
Populations of stars have been aging and evolving, so that distant galaxies (which are observed as they were in the early universe) appear very different from nearby galaxies (observed in a more recent state). Moreover, galaxies that formed relatively recently appear markedly different from galaxies formed at similar distances but shortly after the Big Bang. These observations are strong arguments against the steady-state model. Observations of star formation, galaxy and quasar distributions and larger structures, agree well with Big Bang simulations of the formation of structure in the universe, and are helping to complete details of the theory.	654	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	585	54	2,024	8	10	31	0
In 2011, astronomers found what they believe to be pristine clouds of primordial gas by analyzing absorption lines in the spectra of distant quasars. Before this discovery, all other astronomical objects have been observed to contain heavy elements that are formed in stars. Despite being sensitive to carbon, oxygen, and silicon, these three elements were not detected in these two clouds. Since the clouds of gas have no detectable levels of heavy elements, they likely formed in the first few minutes after the Big Bang, during BBN.	535	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	586	55	2,024	8	10	31	0
The age of the universe as estimated from the Hubble expansion and the CMB is now in agreement with other estimates using the ages of the oldest stars, both as measured by applying the theory of stellar evolution to globular clusters and through radiometric dating of individual Population II stars. It is also in agreement with age estimates based on measurements of the expansion using Type Ia supernovae and measurements of temperature fluctuations in the cosmic microwave background. The agreement of independent measurements of this age supports the Lambda-CDM (ΛCDM) model, since the model is used to relate some of the measurements to an age estimate, and all estimates turn agree. Still, some observations of objects from the relatively early universe (in particular quasar APM 08279+5255) raise concern as to whether these objects had enough time to form so early in the ΛCDM model.	891	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	587	56	2,024	8	10	31	0
The prediction that the CMB temperature was higher in the past has been experimentally supported by observations of very low temperature absorption lines in gas clouds at high redshift. This prediction also implies that the amplitude of the Sunyaev–Zel'dovich effect in clusters of galaxies does not depend directly on redshift. Observations have found this to be roughly true, but this effect depends on cluster properties that do change with cosmic time, making precise measurements difficult.	495	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	588	57	2,024	8	10	31	0
Future gravitational-wave observatories might be able to detect primordial gravitational waves, relics of the early universe, up to less than a second after the Big Bang.	170	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	589	58	2,024	8	10	31	0
As with any theory, a number of mysteries and problems have arisen as a result of the development of the Big Bang models. Some of these mysteries and problems have been resolved while others are still outstanding. Proposed solutions to some of the problems in the Big Bang model have revealed new mysteries of their own. For example, the horizon problem, the magnetic monopole problem, and the flatness problem are most commonly resolved with inflation theory, but the details of the inflationary universe are still left unresolved and many, including some founders of the theory, say it has been disproven. What follows are a list of the mysterious aspects of the Big Bang concept still under intense investigation by cosmologists and astrophysicists.	752	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	590	59	2,024	8	10	31	0
It is not yet understood why the universe has more matter than antimatter. It is generally assumed that when the universe was young and very hot it was in statistical equilibrium and contained equal numbers of baryons and antibaryons. However, observations suggest that the universe, including its most distant parts, is made almost entirely of normal matter, rather than antimatter. A process called baryogenesis was hypothesized to account for the asymmetry. For baryogenesis to occur, the Sakharov conditions must be satisfied. These require that baryon number is not conserved, that C-symmetry and CP-symmetry are violated and that the universe depart from thermodynamic equilibrium. All these conditions occur in the Standard Model, but the effects are not strong enough to explain the present baryon asymmetry.	816	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	591	60	2,024	8	10	31	0
Measurements of the redshift– magnitude relation for type Ia supernovae indicate that the expansion of the universe has been accelerating since the universe was about half its present age. To explain this acceleration, general relativity requires that much of the energy in the universe consists of a component with large negative pressure, dubbed "dark energy".	362	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	592	61	2,024	8	10	31	0
Dark energy, though speculative, solves numerous problems. Measurements of the cosmic microwave background indicate that the universe is very nearly spatially flat, and therefore according to general relativity the universe must have almost exactly the critical density of mass/energy. But the mass density of the universe can be measured from its gravitational clustering, and is found to have only about 30% of the critical density. Since theory suggests that dark energy does not cluster in the usual way it is the best explanation for the "missing" energy density. Dark energy also helps to explain two geometrical measures of the overall curvature of the universe, one using the frequency of gravitational lenses, and the other using the characteristic pattern of the large-scale structure-- baryon acoustic oscillations --as a cosmic ruler.	846	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	593	62	2,024	8	10	31	0
Negative pressure is believed to be a property of vacuum energy, but the exact nature and existence of dark energy remains one of the great mysteries of the Big Bang. Results from the WMAP team in 2008 are in accordance with a universe that consists of 73% dark energy, 23% dark matter, 4.6% regular matter and less than 1% neutrinos. According to theory, the energy density in matter decreases with the expansion of the universe, but the dark energy density remains constant (or nearly so) as the universe expands. Therefore, matter made up a larger fraction of the total energy of the universe in the past than it does today, but its fractional contribution will fall in the far future as dark energy becomes even more dominant.	730	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	594	63	2,024	8	10	31	0
The dark energy component of the universe has been explained by theorists using a variety of competing theories including Einstein's cosmological constant but also extending to more exotic forms of quintessence or other modified gravity schemes. A cosmological constant problem, sometimes called the "most embarrassing problem in physics", results from the apparent discrepancy between the measured energy density of dark energy, and the one naively predicted from Planck units.	478	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	595	64	2,024	8	10	31	1	UNITS
During the 1970s and the 1980s, various observations showed that there is not sufficient visible matter in the universe to account for the apparent strength of gravitational forces within and between galaxies. This led to the idea that up to 90% of the matter in the universe is dark matter that does not emit light or interact with normal baryonic matter. In addition, the assumption that the universe is mostly normal matter led to predictions that were strongly inconsistent with observations. In particular, the universe today is far more lumpy and contains far less deuterium than can be accounted for without dark matter. While dark matter has always been controversial, it is inferred by various observations: the anisotropies in the CMB, galaxy cluster velocity dispersions, large-scale structure distributions, gravitational lensing studies, and X-ray measurements of galaxy clusters.	893	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	596	65	2,024	8	10	31	0
Indirect evidence for dark matter comes from its gravitational influence on other matter, as no dark matter particles have been observed in laboratories. Many particle physics candidates for dark matter have been proposed, and several projects to detect them directly are underway.	281	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	597	66	2,024	8	10	31	0
Additionally, there are outstanding problems associated with the currently favored cold dark matter model which include the dwarf galaxy problem and the cuspy halo problem. Alternative theories have been proposed that do not require a large amount of undetected matter, but instead modify the laws of gravity established by Newton and Einstein; yet no alternative theory has been as successful as the cold dark matter proposal in explaining all extant observations.	465	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	598	67	2,024	8	10	31	0
The horizon problem results from the premise that information cannot travel faster than light. In a universe of finite age this sets a limit—the particle horizon—on the separation of any two regions of space that are in causal contact. The observed isotropy of the CMB is problematic in this regard: if the universe had been dominated by radiation or matter at all times up to the epoch of last scattering, the particle horizon at that time would correspond to about 2 degrees on the sky. There would then be no mechanism to cause wider regions to have the same temperature.	574	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	599	68	2,024	8	10	31	0

By taking into consideration time-varying multistability that is associated with the modulation of large-scale processes (e.g., seasonal forcing) and aggregated feedback of small-scale processes (e.g., convection), the above revised view is refined as follows:

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"The atmosphere possesses chaos and order; it includes, as examples, emerging organized systems (such as tornadoes) and time varying forcing from recurrent seasons."

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The potential for sensitive dependence on initial conditions (the butterfly effect) has been studied in a number of cases in semiclassical and quantum physics, including atoms in strong fields and the anisotropic Kepler problem. Some authors have argued that extreme (exponential) dependence on initial conditions is not expected in pure quantum treatments; however, the sensitive dependence on initial conditions demonstrated in classical motion is included in the semiclassical treatments developed by Martin Gutzwiller and John B. Delos and co-workers. The random matrix theory and simulations with quantum computers prove that some versions of the butterfly effect in quantum mechanics do not exist.

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Other authors suggest that the butterfly effect can be observed in quantum systems. Zbyszek P. Karkuszewski et al. consider the time evolution of quantum systems which have slightly different Hamiltonians. They investigate the level of sensitivity of quantum systems to small changes in their given Hamiltonians. David Poulin et al. presented a quantum algorithm to measure fidelity decay, which "measures the rate at which identical initial states diverge when subjected to slightly different dynamics". They consider fidelity decay to be "the closest quantum analog to the (purely classical) butterfly effect". Whereas the classical butterfly effect considers the effect of a small change in the position and/or velocity of an object in a given Hamiltonian system, the quantum butterfly effect considers the effect of a small change in the Hamiltonian system with a given initial position and velocity. This quantum butterfly effect has been demonstrated experimentally. Quantum and semiclassical treatments of system sensitivity to initial conditions are known as quantum chaos.

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The butterfly effect has appeared across mediums such as literature (for instance, A Sound of Thunder), films and television (such as The Simpsons), video games (such as Life Is Strange), AI-driven expansive language models, and more.

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In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution) is a probability distribution or probability measure that gives the probability that a system will be in a certain state as a function of that state's energy and the temperature of the system. The distribution is expressed in the form:

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where p i is the probability of the system being in state i, exp is the exponential function, ε i is the energy of that state, and a constant kT of the distribution is the product of the Boltzmann constant k and thermodynamic temperature T. The symbol ∝ ∝ denotes proportionality (see § The distribution for the proportionality constant).

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The term system here has a wide meaning; it can range from a collection of 'sufficient number' of atoms or a single atom to a macroscopic system such as a natural gas storage tank. Therefore the Boltzmann distribution can be used to solve a wide variety of problems. The distribution shows that states with lower energy will always have a higher probability of being occupied.

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The ratio of probabilities of two states is known as the Boltzmann factor and characteristically only depends on the states' energy difference:

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The Boltzmann distribution is named after Ludwig Boltzmann who first formulated it in 1868 during his studies of the statistical mechanics of gases in thermal equilibrium. Boltzmann's statistical work is borne out in his paper “On the Relationship between the Second Fundamental Theorem of the Mechanical Theory of Heat and Probability Calculations Regarding the Conditions for Thermal Equilibrium" The distribution was later investigated extensively, in its modern generic form, by Josiah Willard Gibbs in 1902.

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The Boltzmann distribution should not be confused with the Maxwell–Boltzmann distribution or Maxwell-Boltzmann statistics. The Boltzmann distribution gives the probability that a system will be in a certain state as a function of that state's energy, while the Maxwell-Boltzmann distributions give the probabilities of particle speeds or energies in ideal gases. The distribution of energies in a one-dimensional gas however, does follow the Boltzmann distribution.

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The Boltzmann distribution is a probability distribution that gives the probability of a certain state as a function of that state's energy and temperature of the system to which the distribution is applied. It is given as p i = 1 Q exp ⁡ ⁡ ( − − ε ε i k T ) = exp ⁡ ⁡ ( − − ε ε i k T ) ∑ ∑ j = 1 M exp ⁡ ⁡ ( − − ε ε j k T )

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where:

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Using Lagrange multipliers, one can prove that the Boltzmann distribution is the distribution that maximizes the entropy S ( p 1 , p 2 , ⋯ ⋯ , p M ) = − − ∑ ∑ i = 1 M p i log 2 ⁡ ⁡ p i

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subject to the normalization constraint that ∑ ∑ p i = 1 and the constraint that ∑ ∑ p i ε ε i equals a particular mean energy value, except for two special cases. (These special cases occur when the mean value is either the minimum or maximum of the energies ε i. In these cases, the entropy maximizing distribution is a limit of Boltzmann distributions where T approaches zero from above or below, respectively.)

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The partition function can be calculated if we know the energies of the states accessible to the system of interest. For atoms the partition function values can be found in the NIST Atomic Spectra Database.

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The distribution shows that states with lower energy will always have a higher probability of being occupied than the states with higher energy. It can also give us the quantitative relationship between the probabilities of the two states being occupied. The ratio of probabilities for states i and j is given as p i p j = exp ⁡ ⁡ ( ε ε j − − ε ε i k T )

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where:

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The corresponding ratio of populations of energy levels must also take their degeneracies into account.

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The Boltzmann distribution is often used to describe the distribution of particles, such as atoms or molecules, over bound states accessible to them. If we have a system consisting of many particles, the probability of a particle being in state i is practically the probability that, if we pick a random particle from that system and check what state it is in, we will find it is in state i. This probability is equal to the number of particles in state i divided by the total number of particles in the system, that is the fraction of particles that occupy state i.

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where N i is the number of particles in state i and N is the total number of particles in the system. We may use the Boltzmann distribution to find this probability that is, as we have seen, equal to the fraction of particles that are in state i. So the equation that gives the fraction of particles in state i as a function of the energy of that state is N i N = exp ⁡ ⁡ ( − − ε ε i k T ) ∑ ∑ j = 1 M exp ⁡ ⁡ ( − − ε ε j k T )

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This equation is of great importance to spectroscopy. In spectroscopy we observe a spectral line of atoms or molecules undergoing transitions from one state to another. In order for this to be possible, there must be some particles in the first state to undergo the transition. We may find that this condition is fulfilled by finding the fraction of particles in the first state. If it is negligible, the transition is very likely not observed at the temperature for which the calculation was done. In general, a larger fraction of molecules in the first state means a higher number of transitions to the second state. This gives a stronger spectral line. However, there are other factors that influence the intensity of a spectral line, such as whether it is caused by an allowed or a forbidden transition.

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The softmax function commonly used in machine learning is related to the Boltzmann distribution:

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Distribution of the form

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is called generalized Boltzmann distribution by some authors.

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The Boltzmann distribution is a special case of the generalized Boltzmann distribution. The generalized Boltzmann distribution is used in statistical mechanics to describe canonical ensemble, grand canonical ensemble and isothermal–isobaric ensemble. The generalized Boltzmann distribution is usually derived from the principle of maximum entropy, but there are other derivations.

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The generalized Boltzmann distribution has the following properties:

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The Boltzmann distribution appears in statistical mechanics when considering closed systems of fixed composition that are in thermal equilibrium (equilibrium with respect to energy exchange). The most general case is the probability distribution for the canonical ensemble. Some special cases (derivable from the canonical ensemble) show the Boltzmann distribution in different aspects:

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Although these cases have strong similarities, it is helpful to distinguish them as they generalize in different ways when the crucial assumptions are changed:

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The Boltzmann distribution can be introduced to allocate permits in emissions trading. The new allocation method using the Boltzmann distribution can describe the most probable, natural, and unbiased distribution of emissions permits among multiple countries.

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The Boltzmann distribution has the same form as the multinomial logit model. As a discrete choice model, this is very well known in economics since Daniel McFadden made the connection to random utility maximization.

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The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. It was first proposed as a physical theory in 1931 by Roman Catholic priest and physicist Georges Lemaître when he suggested the universe emerged from a "primeval atom". Various cosmological models of the Big Bang explain the evolution of the observable universe from the earliest known periods through its subsequent large-scale form. These models offer a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure. The uniformity of the universe, known as the flatness problem, is explained through cosmic inflation : a sudden and very rapid expansion of space during the earliest moments.

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Crucially, these models are compatible with the Hubble–Lemaître law —the observation that the farther away a galaxy is, the faster it is moving away from Earth. Extrapolating this cosmic expansion backward in time using the known laws of physics, the models describe an increasingly concentrated cosmos preceded by a singularity in which space and time lose meaning (typically named "the Big Bang singularity"). Physics lacks a widely accepted theory of quantum gravity that can model the earliest conditions of the Big Bang. In 1964 the CMB was discovered, which convinced many cosmologists that the competing steady-state model of cosmic evolution was falsified, since the Big Bang models predict a uniform background radiation caused by high temperatures and densities in the distant past. A wide range of empirical evidence strongly favors the Big Bang event, which is now essentially universally accepted. Detailed measurements of the expansion rate of the universe place the Big Bang singularity at an estimated 13.787 ± 0.020 billion years ago, which is considered the age of the universe.

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There remain aspects of the observed universe that are not yet adequately explained by the Big Bang models. After its initial expansion, the universe cooled sufficiently to allow the formation of subatomic particles, and later atoms. The unequal abundances of matter and antimatter that allowed this to occur is an unexplained effect known as baryon asymmetry. These primordial elements—mostly hydrogen, with some helium and lithium —later coalesced through gravity, forming early stars and galaxies. Astronomers observe the gravitational effects of an unknown dark matter surrounding galaxies. Most of the gravitational potential in the universe seems to be in this form, and the Big Bang models and various observations indicate that this excess gravitational potential is not created by baryonic matter, such as normal atoms. Measurements of the redshifts of supernovae indicate that the expansion of the universe is accelerating, an observation attributed to an unexplained phenomenon known as dark energy.

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The Big Bang models offer a comprehensive explanation for a broad range of observed phenomena, including the abundances of the light elements, the CMB, large-scale structure, and Hubble's law. The models depend on two major assumptions: the universality of physical laws and the cosmological principle. The universality of physical laws is one of the underlying principles of the theory of relativity. The cosmological principle states that on large scales the universe is homogeneous and isotropic —appearing the same in all directions regardless of location.

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These ideas were initially taken as postulates, but later efforts were made to test each of them. For example, the first assumption has been tested by observations showing that the largest possible deviation of the fine-structure constant over much of the age of the universe is of order 10. Also, general relativity has passed stringent tests on the scale of the Solar System and binary stars.

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The large-scale universe appears isotropic as viewed from Earth. If it is indeed isotropic, the cosmological principle can be derived from the simpler Copernican principle, which states that there is no preferred (or special) observer or vantage point. To this end, the cosmological principle has been confirmed to a level of 10 via observations of the temperature of the CMB. At the scale of the CMB horizon, the universe has been measured to be homogeneous with an upper bound on the order of 10% inhomogeneity, as of 1995.

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An important feature of the Big Bang spacetime is the presence of particle horizons. Since the universe has a finite age, and light travels at a finite speed, there may be events in the past whose light has not yet had time to reach earth. This places a limit or a past horizon on the most distant objects that can be observed. Conversely, because space is expanding, and more distant objects are receding ever more quickly, light emitted by us today may never "catch up" to very distant objects. This defines a future horizon, which limits the events in the future that we will be able to influence. The presence of either type of horizon depends on the details of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric that describes the expansion of the universe.

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Our understanding of the universe back to very early times suggests that there is a past horizon, though in practice our view is also limited by the opacity of the universe at early times. So our view cannot extend further backward in time, though the horizon recedes in space. If the expansion of the universe continues to accelerate, there is a future horizon as well.

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Some processes in the early universe occurred too slowly, compared to the expansion rate of the universe, to reach approximate thermodynamic equilibrium. Others were fast enough to reach thermalization. The parameter usually used to find out whether a process in the very early universe has reached thermal equilibrium is the ratio between the rate of the process (usually rate of collisions between particles) and the Hubble parameter. The larger the ratio, the more time particles had to thermalize before they were too far away from each other.

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According to the Big Bang models, the universe at the beginning was very hot and very compact, and since then it has been expanding and cooling.

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In the absence of a perfect cosmological principle, extrapolation of the expansion of the universe backwards in time using general relativity yields an infinite density and temperature at a finite time in the past. This irregular behavior, known as the gravitational singularity, indicates that general relativity is not an adequate description of the laws of physics in this regime. Models based on general relativity alone cannot fully extrapolate toward the singularity. In some proposals, such as the emergent Universe models, the singularity is replaced by another cosmological epoch. A different approach identifies the initial singularity as a singularity predicted by some models of the Big Bang theory to have existed before the Big Bang event.

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This primordial singularity is itself sometimes called "the Big Bang", but the term can also refer to a more generic early hot, dense phase of the universe. In either case, "the Big Bang" as an event is also colloquially referred to as the "birth" of our universe since it represents the point in history where the universe can be verified to have entered into a regime where the laws of physics as we understand them (specifically general relativity and the Standard Model of particle physics) work. Based on measurements of the expansion using Type Ia supernovae and measurements of temperature fluctuations in the cosmic microwave background, the time that has passed since that event—known as the " age of the universe "—is 13.8 billion years.

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Despite being extremely dense at this time—far denser than is usually required to form a black hole —the universe did not re-collapse into a singularity. Commonly used calculations and limits for explaining gravitational collapse are usually based upon objects of relatively constant size, such as stars, and do not apply to rapidly expanding space such as the Big Bang. Since the early universe did not immediately collapse into a multitude of black holes, matter at that time must have been very evenly distributed with a negligible density gradient.

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The earliest phases of the Big Bang are subject to much speculation, given the lack of available data. In the most common models the universe was filled homogeneously and isotropically with a very high energy density and huge temperatures and pressures, and was very rapidly expanding and cooling. The period up to 10 seconds into the expansion, the Planck epoch, was a phase in which the four fundamental forces —the electromagnetic force, the strong nuclear force, the weak nuclear force, and the gravitational force, were unified as one. In this stage, the characteristic scale length of the universe was the Planck length, 1.6 × 10 m, and consequently had a temperature of approximately 10 degrees Celsius. Even the very concept of a particle breaks down in these conditions. A proper understanding of this period awaits the development of a theory of quantum gravity. The Planck epoch was succeeded by the grand unification epoch beginning at 10 seconds, where gravitation separated from the other forces as the universe's temperature fell.

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3

EPOCH, UNITS, EPOCH

At approximately 10 seconds into the expansion, a phase transition caused a cosmic inflation, during which the universe grew exponentially, unconstrained by the light speed invariance, and temperatures dropped by a factor of 100,000. This concept is motivated by the flatness problem, where the density of matter and energy is very close to the critical density needed to produce a flat universe. That is, the shape of the universe has no overall geometric curvature due to gravitational influence. Microscopic quantum fluctuations that occurred because of Heisenberg's uncertainty principle were "frozen in" by inflation, becoming amplified into the seeds that would later form the large-scale structure of the universe. At a time around 10 seconds, the electroweak epoch begins when the strong nuclear force separates from the other forces, with only the electromagnetic force and weak nuclear force remaining unified.

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Inflation stopped locally at around 10 to 10 seconds, with the observable universe's volume having increased by a factor of at least 10. Reheating followed as the inflaton field decayed, until the universe obtained the temperatures required for the production of a quark–gluon plasma as well as all other elementary particles. Temperatures were so high that the random motions of particles were at relativistic speeds, and particle–antiparticle pairs of all kinds were being continuously created and destroyed in collisions. At some point, an unknown reaction called baryogenesis violated the conservation of baryon number, leading to a very small excess of quarks and leptons over antiquarks and antileptons—of the order of one part in 30 million. This resulted in the predominance of matter over antimatter in the present universe.

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The universe continued to decrease in density and fall in temperature, hence the typical energy of each particle was decreasing. Symmetry-breaking phase transitions put the fundamental forces of physics and the parameters of elementary particles into their present form, with the electromagnetic force and weak nuclear force separating at about 10 seconds.

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After about 10 seconds, the picture becomes less speculative, since particle energies drop to values that can be attained in particle accelerators. At about 10 seconds, quarks and gluons combined to form baryons such as protons and neutrons. The small excess of quarks over antiquarks led to a small excess of baryons over antibaryons. The temperature was no longer high enough to create either new proton–antiproton or neutron–antineutron pairs. A mass annihilation immediately followed, leaving just one in 10 of the original matter particles and none of their antiparticles. A similar process happened at about 1 second for electrons and positrons. After these annihilations, the remaining protons, neutrons and electrons were no longer moving relativistically and the energy density of the universe was dominated by photons (with a minor contribution from neutrinos).

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A few minutes into the expansion, when the temperature was about a billion kelvin and the density of matter in the universe was comparable to the current density of Earth's atmosphere, neutrons combined with protons to form the universe's deuterium and helium nuclei in a process called Big Bang nucleosynthesis (BBN). Most protons remained uncombined as hydrogen nuclei.

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As the universe cooled, the rest energy density of matter came to gravitationally dominate that of the photon radiation. The recombination epoch began after about 379,000 years, when the electrons and nuclei combined into atoms (mostly hydrogen), which were able to emit radiation. This relic radiation, which continued through space largely unimpeded, is known as the cosmic microwave background.

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After the recombination epoch, the slightly denser regions of the uniformly distributed matter gravitationally attracted nearby matter and thus grew even denser, forming gas clouds, stars, galaxies, and the other astronomical structures observable today. The details of this process depend on the amount and type of matter in the universe. The four possible types of matter are known as cold dark matter (CDM), warm dark matter, hot dark matter, and baryonic matter. The best measurements available, from the Wilkinson Microwave Anisotropy Probe (WMAP), show that the data is well-fit by a Lambda-CDM model in which dark matter is assumed to be cold. (Warm dark matter is ruled out by early reionization.) This CDM is estimated to make up about 23% of the matter/energy of the universe, while baryonic matter makes up about 4.6%.

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In an "extended model" which includes hot dark matter in the form of neutrinos, then the "physical baryon density" Ω Ω b h 2 is estimated at 0.023. (This is different from the 'baryon density' Ω Ω b expressed as a fraction of the total matter/energy density, which is about 0.046.) The corresponding cold dark matter density Ω Ω c h 2 is about 0.11, and the corresponding neutrino density Ω Ω v h 2 is estimated to be less than 0.0062.

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Independent lines of evidence from Type Ia supernovae and the CMB imply that the universe today is dominated by a mysterious form of energy known as dark energy, which appears to homogeneously permeate all of space. Observations suggest that 73% of the total energy density of the present day universe is in this form. When the universe was very young it was likely infused with dark energy, but with everything closer together, gravity predominated, braking the expansion. Eventually, after billions of years of expansion, the declining density of matter relative to the density of dark energy allowed the expansion of the universe to begin to accelerate.

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Dark energy in its simplest formulation is modeled by a cosmological constant term in Einstein field equations of general relativity, but its composition and mechanism are unknown. More generally, the details of its equation of state and relationship with the Standard Model of particle physics continue to be investigated both through observation and theory.

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All of this cosmic evolution after the inflationary epoch can be rigorously described and modeled by the lambda-CDM model of cosmology, which uses the independent frameworks of quantum mechanics and general relativity. There are no easily testable models that would describe the situation prior to approximately 10 seconds. Understanding this earliest of eras in the history of the universe is one of the greatest unsolved problems in physics.

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English astronomer Fred Hoyle is credited with coining the term "Big Bang" during a talk for a March 1949 BBC Radio broadcast, saying: "These theories were based on the hypothesis that all the matter in the universe was created in one big bang at a particular time in the remote past." However, it did not catch on until the 1970s.

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It is popularly reported that Hoyle, who favored an alternative " steady-state " cosmological model, intended this to be pejorative, but Hoyle explicitly denied this and said it was just a striking image meant to highlight the difference between the two models. Helge Kragh writes that the evidence for the claim that it was meant as a pejorative is "unconvincing", and mentions a number of indications that it was not a pejorative.

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The term itself has been argued to be a misnomer because it evokes an explosion. The argument is that whereas an explosion suggests expansion into a surrounding space, the Big Bang only describes the intrinsic expansion of the contents of the universe. Another issue pointed out by Santhosh Mathew is that bang implies sound, which is not an important feature of the model. An attempt to find a more suitable alternative was not successful.

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The Big Bang models developed from observations of the structure of the universe and from theoretical considerations. In 1912, Vesto Slipher measured the first Doppler shift of a " spiral nebula " (spiral nebula is the obsolete term for spiral galaxies), and soon discovered that almost all such nebulae were receding from Earth. He did not grasp the cosmological implications of this fact, and indeed at the time it was highly controversial whether or not these nebulae were "island universes" outside our Milky Way. Ten years later, Alexander Friedmann, a Russian cosmologist and mathematician, derived the Friedmann equations from the Einstein field equations, showing that the universe might be expanding in contrast to the static universe model advocated by Albert Einstein at that time.

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In 1924, American astronomer Edwin Hubble 's measurement of the great distance to the nearest spiral nebulae showed that these systems were indeed other galaxies. Starting that same year, Hubble painstakingly developed a series of distance indicators, the forerunner of the cosmic distance ladder, using the 100-inch (2.5 m) Hooker telescope at Mount Wilson Observatory. This allowed him to estimate distances to galaxies whose redshifts had already been measured, mostly by Slipher. In 1929, Hubble discovered a correlation between distance and recessional velocity —now known as Hubble's law.

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Independently deriving Friedmann's equations in 1927, Georges Lemaître, a Belgian physicist and Roman Catholic priest, proposed that the recession of the nebulae was due to the expansion of the universe. He inferred the relation that Hubble would later observe, given the cosmological principle. In 1931, Lemaître went further and suggested that the evident expansion of the universe, if projected back in time, meant that the further in the past the smaller the universe was, until at some finite time in the past all the mass of the universe was concentrated into a single point, a "primeval atom" where and when the fabric of time and space came into existence.

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In the 1920s and 1930s, almost every major cosmologist preferred an eternal steady-state universe, and several complained that the beginning of time implied by the Big Bang imported religious concepts into physics; this objection was later repeated by supporters of the steady-state theory. This perception was enhanced by the fact that the originator of the Big Bang concept, Lemaître, was a Roman Catholic priest. Arthur Eddington agreed with Aristotle that the universe did not have a beginning in time, viz., that matter is eternal. A beginning in time was "repugnant" to him. Lemaître, however, disagreed:

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If the world has begun with a single quantum, the notions of space and time would altogether fail to have any meaning at the beginning; they would only begin to have a sensible meaning when the original quantum had been divided into a sufficient number of quanta. If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time.

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During the 1930s, other ideas were proposed as non-standard cosmologies to explain Hubble's observations, including the Milne model, the oscillatory universe (originally suggested by Friedmann, but advocated by Albert Einstein and Richard C. Tolman) and Fritz Zwicky 's tired light hypothesis.

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After World War II, two distinct possibilities emerged. One was Fred Hoyle's steady-state model, whereby new matter would be created as the universe seemed to expand. In this model the universe is roughly the same at any point in time. The other was Lemaître's Big Bang theory, advocated and developed by George Gamow, who introduced BBN and whose associates, Ralph Alpher and Robert Herman, predicted the CMB. Ironically, it was Hoyle who coined the phrase that came to be applied to Lemaître's theory, referring to it as "this big bang idea" during a BBC Radio broadcast in March 1949. For a while, support was split between these two theories. Eventually, the observational evidence, most notably from radio source counts, began to favor Big Bang over steady state. The discovery and confirmation of the CMB in 1964 secured the Big Bang as the best theory of the origin and evolution of the universe.

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In 1968 and 1970, Roger Penrose, Stephen Hawking, and George F. R. Ellis published papers where they showed that mathematical singularities were an inevitable initial condition of relativistic models of the Big Bang. Then, from the 1970s to the 1990s, cosmologists worked on characterizing the features of the Big Bang universe and resolving outstanding problems. In 1981, Alan Guth made a breakthrough in theoretical work on resolving certain outstanding theoretical problems in the Big Bang models with the introduction of an epoch of rapid expansion in the early universe he called "inflation". Meanwhile, during these decades, two questions in observational cosmology that generated much discussion and disagreement were over the precise values of the Hubble Constant and the matter-density of the universe (before the discovery of dark energy, thought to be the key predictor for the eventual fate of the universe).

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In the mid-1990s, observations of certain globular clusters appeared to indicate that they were about 15 billion years old, which conflicted with most then-current estimates of the age of the universe (and indeed with the age measured today). This issue was later resolved when new computer simulations, which included the effects of mass loss due to stellar winds, indicated a much younger age for globular clusters.

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Significant progress in Big Bang cosmology has been made since the late 1990s as a result of advances in telescope technology as well as the analysis of data from satellites such as the Cosmic Background Explorer (COBE), the Hubble Space Telescope and WMAP. Cosmologists now have fairly precise and accurate measurements of many of the parameters of the Big Bang model, and have made the unexpected discovery that the expansion of the universe appears to be accelerating.

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"[The] big bang picture is too firmly grounded in data from every area to be proved invalid in its general features."

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— Lawrence Krauss

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The earliest and most direct observational evidence of the validity of the theory are the expansion of the universe according to Hubble's law (as indicated by the redshifts of galaxies), discovery and measurement of the cosmic microwave background and the relative abundances of light elements produced by Big Bang nucleosynthesis (BBN). More recent evidence includes observations of galaxy formation and evolution, and the distribution of large-scale cosmic structures, These are sometimes called the "four pillars" of the Big Bang models.

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Precise modern models of the Big Bang appeal to various exotic physical phenomena that have not been observed in terrestrial laboratory experiments or incorporated into the Standard Model of particle physics. Of these features, dark matter is currently the subject of most active laboratory investigations. Remaining issues include the cuspy halo problem and the dwarf galaxy problem of cold dark matter. Dark energy is also an area of intense interest for scientists, but it is not clear whether direct detection of dark energy will be possible. Inflation and baryogenesis remain more speculative features of current Big Bang models. Viable, quantitative explanations for such phenomena are still being sought. These are unsolved problems in physics.

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Observations of distant galaxies and quasars show that these objects are redshifted: the light emitted from them has been shifted to longer wavelengths. This can be seen by taking a frequency spectrum of an object and matching the spectroscopic pattern of emission or absorption lines corresponding to atoms of the chemical elements interacting with the light. These redshifts are uniformly isotropic, distributed evenly among the observed objects in all directions. If the redshift is interpreted as a Doppler shift, the recessional velocity of the object can be calculated. For some galaxies, it is possible to estimate distances via the cosmic distance ladder. When the recessional velocities are plotted against these distances, a linear relationship known as Hubble's law is observed: v = H 0 D where

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Hubble's law implies that the universe is uniformly expanding everywhere. This cosmic expansion was predicted from general relativity by Friedmann in 1922 and Lemaître in 1927, well before Hubble made his 1929 analysis and observations, and it remains the cornerstone of the Big Bang model as developed by Friedmann, Lemaître, Robertson, and Walker.

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The theory requires the relation v = H D to hold at all times, where D is the proper distance, v is the recessional velocity, and v , H , and D vary as the universe expands (hence we write H 0 to denote the present-day Hubble "constant"). For distances much smaller than the size of the observable universe, the Hubble redshift can be thought of as the Doppler shift corresponding to the recession velocity v . For distances comparable to the size of the observable universe, the attribution of the cosmological redshift becomes more ambiguous, although its interpretation as a kinematic Doppler shift remains the most natural one.

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An unexplained discrepancy with the determination of the Hubble constant is known as Hubble tension. Techniques based on observation of the CMB suggest a lower value of this constant compared to the quantity derived from measurements based on the cosmic distance ladder.

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In 1964, Arno Penzias and Robert Wilson serendipitously discovered the cosmic background radiation, an omnidirectional signal in the microwave band. Their discovery provided substantial confirmation of the big-bang predictions by Alpher, Herman and Gamow around 1950. Through the 1970s, the radiation was found to be approximately consistent with a blackbody spectrum in all directions; this spectrum has been redshifted by the expansion of the universe, and today corresponds to approximately 2.725 K. This tipped the balance of evidence in favor of the Big Bang model, and Penzias and Wilson were awarded the 1978 Nobel Prize in Physics.

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The surface of last scattering corresponding to emission of the CMB occurs shortly after recombination, the epoch when neutral hydrogen becomes stable. Prior to this, the universe comprised a hot dense photon-baryon plasma sea where photons were quickly scattered from free charged particles. Peaking at around 372 ± 14 kyr, the mean free path for a photon becomes long enough to reach the present day and the universe becomes transparent.

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In 1989, NASA launched COBE, which made two major advances: in 1990, high-precision spectrum measurements showed that the CMB frequency spectrum is an almost perfect blackbody with no deviations at a level of 1 part in 10, and measured a residual temperature of 2.726 K (more recent measurements have revised this figure down slightly to 2.7255 K); then in 1992, further COBE measurements discovered tiny fluctuations (anisotropies) in the CMB temperature across the sky, at a level of about one part in 10. John C. Mather and George Smoot were awarded the 2006 Nobel Prize in Physics for their leadership in these results.

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During the following decade, CMB anisotropies were further investigated by a large number of ground-based and balloon experiments. In 2000–2001, several experiments, most notably BOOMERanG, found the shape of the universe to be spatially almost flat by measuring the typical angular size (the size on the sky) of the anisotropies.

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In early 2003, the first results of the Wilkinson Microwave Anisotropy Probe were released, yielding what were at the time the most accurate values for some of the cosmological parameters. The results disproved several specific cosmic inflation models, but are consistent with the inflation theory in general. The Planck space probe was launched in May 2009. Other ground and balloon-based cosmic microwave background experiments are ongoing.

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Using Big Bang models, it is possible to calculate the expected concentration of the isotopes helium-4 (He), helium-3 (He), deuterium (H), and lithium-7 (Li) in the universe as ratios to the amount of ordinary hydrogen. The relative abundances depend on a single parameter, the ratio of photons to baryons. This value can be calculated independently from the detailed structure of CMB fluctuations. The ratios predicted (by mass, not by abundance) are about 0.25 for He:H, about 10 for H:H, about 10 for He:H, and about 10 for Li:H.

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The measured abundances all agree at least roughly with those predicted from a single value of the baryon-to-photon ratio. The agreement is excellent for deuterium, close but formally discrepant for He, and off by a factor of two for Li (this anomaly is known as the cosmological lithium problem); in the latter two cases, there are substantial systematic uncertainties. Nonetheless, the general consistency with abundances predicted by BBN is strong evidence for the Big Bang, as the theory is the only known explanation for the relative abundances of light elements, and it is virtually impossible to "tune" the Big Bang to produce much more or less than 20–30% helium. Indeed, there is no obvious reason outside of the Big Bang that, for example, the young universe before star formation, as determined by studying matter supposedly free of stellar nucleosynthesis products, should have more helium than deuterium or more deuterium than He, and in constant ratios, too.

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Detailed observations of the morphology and distribution of galaxies and quasars are in agreement with the current Big Bang models. A combination of observations and theory suggest that the first quasars and galaxies formed within a billion years after the Big Bang, and since then, larger structures have been forming, such as galaxy clusters and superclusters.

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Populations of stars have been aging and evolving, so that distant galaxies (which are observed as they were in the early universe) appear very different from nearby galaxies (observed in a more recent state). Moreover, galaxies that formed relatively recently appear markedly different from galaxies formed at similar distances but shortly after the Big Bang. These observations are strong arguments against the steady-state model. Observations of star formation, galaxy and quasar distributions and larger structures, agree well with Big Bang simulations of the formation of structure in the universe, and are helping to complete details of the theory.

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In 2011, astronomers found what they believe to be pristine clouds of primordial gas by analyzing absorption lines in the spectra of distant quasars. Before this discovery, all other astronomical objects have been observed to contain heavy elements that are formed in stars. Despite being sensitive to carbon, oxygen, and silicon, these three elements were not detected in these two clouds. Since the clouds of gas have no detectable levels of heavy elements, they likely formed in the first few minutes after the Big Bang, during BBN.

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The age of the universe as estimated from the Hubble expansion and the CMB is now in agreement with other estimates using the ages of the oldest stars, both as measured by applying the theory of stellar evolution to globular clusters and through radiometric dating of individual Population II stars. It is also in agreement with age estimates based on measurements of the expansion using Type Ia supernovae and measurements of temperature fluctuations in the cosmic microwave background. The agreement of independent measurements of this age supports the Lambda-CDM (ΛCDM) model, since the model is used to relate some of the measurements to an age estimate, and all estimates turn agree. Still, some observations of objects from the relatively early universe (in particular quasar APM 08279+5255) raise concern as to whether these objects had enough time to form so early in the ΛCDM model.

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The prediction that the CMB temperature was higher in the past has been experimentally supported by observations of very low temperature absorption lines in gas clouds at high redshift. This prediction also implies that the amplitude of the Sunyaev–Zel'dovich effect in clusters of galaxies does not depend directly on redshift. Observations have found this to be roughly true, but this effect depends on cluster properties that do change with cosmic time, making precise measurements difficult.

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Future gravitational-wave observatories might be able to detect primordial gravitational waves, relics of the early universe, up to less than a second after the Big Bang.

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As with any theory, a number of mysteries and problems have arisen as a result of the development of the Big Bang models. Some of these mysteries and problems have been resolved while others are still outstanding. Proposed solutions to some of the problems in the Big Bang model have revealed new mysteries of their own. For example, the horizon problem, the magnetic monopole problem, and the flatness problem are most commonly resolved with inflation theory, but the details of the inflationary universe are still left unresolved and many, including some founders of the theory, say it has been disproven. What follows are a list of the mysterious aspects of the Big Bang concept still under intense investigation by cosmologists and astrophysicists.

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It is not yet understood why the universe has more matter than antimatter. It is generally assumed that when the universe was young and very hot it was in statistical equilibrium and contained equal numbers of baryons and antibaryons. However, observations suggest that the universe, including its most distant parts, is made almost entirely of normal matter, rather than antimatter. A process called baryogenesis was hypothesized to account for the asymmetry. For baryogenesis to occur, the Sakharov conditions must be satisfied. These require that baryon number is not conserved, that C-symmetry and CP-symmetry are violated and that the universe depart from thermodynamic equilibrium. All these conditions occur in the Standard Model, but the effects are not strong enough to explain the present baryon asymmetry.

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Measurements of the redshift– magnitude relation for type Ia supernovae indicate that the expansion of the universe has been accelerating since the universe was about half its present age. To explain this acceleration, general relativity requires that much of the energy in the universe consists of a component with large negative pressure, dubbed "dark energy".

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Dark energy, though speculative, solves numerous problems. Measurements of the cosmic microwave background indicate that the universe is very nearly spatially flat, and therefore according to general relativity the universe must have almost exactly the critical density of mass/energy. But the mass density of the universe can be measured from its gravitational clustering, and is found to have only about 30% of the critical density. Since theory suggests that dark energy does not cluster in the usual way it is the best explanation for the "missing" energy density. Dark energy also helps to explain two geometrical measures of the overall curvature of the universe, one using the frequency of gravitational lenses, and the other using the characteristic pattern of the large-scale structure-- baryon acoustic oscillations --as a cosmic ruler.

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Negative pressure is believed to be a property of vacuum energy, but the exact nature and existence of dark energy remains one of the great mysteries of the Big Bang. Results from the WMAP team in 2008 are in accordance with a universe that consists of 73% dark energy, 23% dark matter, 4.6% regular matter and less than 1% neutrinos. According to theory, the energy density in matter decreases with the expansion of the universe, but the dark energy density remains constant (or nearly so) as the universe expands. Therefore, matter made up a larger fraction of the total energy of the universe in the past than it does today, but its fractional contribution will fall in the far future as dark energy becomes even more dominant.

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The dark energy component of the universe has been explained by theorists using a variety of competing theories including Einstein's cosmological constant but also extending to more exotic forms of quintessence or other modified gravity schemes. A cosmological constant problem, sometimes called the "most embarrassing problem in physics", results from the apparent discrepancy between the measured energy density of dark energy, and the one naively predicted from Planck units.

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During the 1970s and the 1980s, various observations showed that there is not sufficient visible matter in the universe to account for the apparent strength of gravitational forces within and between galaxies. This led to the idea that up to 90% of the matter in the universe is dark matter that does not emit light or interact with normal baryonic matter. In addition, the assumption that the universe is mostly normal matter led to predictions that were strongly inconsistent with observations. In particular, the universe today is far more lumpy and contains far less deuterium than can be accounted for without dark matter. While dark matter has always been controversial, it is inferred by various observations: the anisotropies in the CMB, galaxy cluster velocity dispersions, large-scale structure distributions, gravitational lensing studies, and X-ray measurements of galaxy clusters.

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Indirect evidence for dark matter comes from its gravitational influence on other matter, as no dark matter particles have been observed in laboratories. Many particle physics candidates for dark matter have been proposed, and several projects to detect them directly are underway.

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Additionally, there are outstanding problems associated with the currently favored cold dark matter model which include the dwarf galaxy problem and the cuspy halo problem. Alternative theories have been proposed that do not require a large amount of undetected matter, but instead modify the laws of gravity established by Newton and Einstein; yet no alternative theory has been as successful as the cold dark matter proposal in explaining all extant observations.

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The horizon problem results from the premise that information cannot travel faster than light. In a universe of finite age this sets a limit—the particle horizon—on the separation of any two regions of space that are in causal contact. The observed isotropy of the CMB is problematic in this regard: if the universe had been dominated by radiation or matter at all times up to the epoch of last scattering, the particle horizon at that time would correspond to about 2 degrees on the sky. There would then be no mechanism to cause wider regions to have the same temperature.

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