Split (1)

train · 102k rows

text large_stringlengths 1 3.58k	length int64 1 3.58k	page_title large_stringlengths 3 128	url large_stringlengths 33 158	text_id int64 0 102k	paragraph_idx int64 0 509	year int64 2.02k 2.02k	month int64 8 8	day int64 10 10	minute int64 30 54	num_planck_labels int64 0 13	planck_labels large_stringclasses 84 values
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...	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 P...	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 express...	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 proporti...	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 ...	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 ...	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 p...	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...	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 ...	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...	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 th...	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 func...	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 fulfill...	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 pr...	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 canonic...	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...	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 sin...	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 unexp...	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 ...	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...	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 lev...	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 ob...	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...	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 i...	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...	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 unive...	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 appl...	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 se...	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 ene...	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 part...	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 f...	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 ov...	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). M...	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 ...	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 matt...	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 den...	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. W...	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 investigat...	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 secon...	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...	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...	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 s...	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 fr...	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....	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 f...	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 ...	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 worl...	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, w...	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 u...	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 t...	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...	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 nucle...	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 iss...	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 chemi...	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, Lem...	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 r...	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 app...	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 ...	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...	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 ani...	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...	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 ca...	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 case...	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, ...	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 d...	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, an...	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 agreem...	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 r...	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....	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...	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 larg...	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 univer...	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...	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 p...	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 i...	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...	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 ...	574	Big_Bang	https://en.wikipedia.org/wiki/Big_Bang	599	68	2,024	8	10	31	0

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.