In cosmology, the Big Bang is the beginning of the universe , i.e. the starting point for the creation of matter, space and time. According to the standard cosmological model , the Big Bang occurred about 13.8 billion years ago. Big Bang theories do not describe the Big Bang itself, but the early universe in its temporal development after the Big Bang.
“Big Bang” does not refer to an explosion in an existing space, but rather the joint creation of matter, space and time from an original singularity . This results formally by considering the development of the expanding universe backwards in time to the point at which the matter and energy density becomes infinite. Accordingly, shortly after the Big Bang, the density of the universe must have exceeded the Planck density . The general theory of relativity is insufficient for the description of this state of affairs; however, it is expected that a theory of quantum gravity still to be developed will do this. Hence, in today's physics there is no generally accepted description of the very early universe, the Big Bang itself, or a time before the Big Bang.
Big Bang theories deal with the development of the universe from a point in time more than one Planck time (about 10 −43 seconds) after the Big Bang to about 300,000 to 400,000 years later, when stable atoms could form and the universe became transparent. The further development is no longer counted as part of the Big Bang.
The Big Bang theories are based on two basic assumptions : The first assumption is that the laws of nature are universal and that the universe can be described with the laws of nature that apply today near Earth. The second assumption is that the universe looks the same in any location (but not at all times) in all directions for great distances. This assumption is called the Copernican principle or the cosmological principle . These assumptions and the basic implications are explained below.
Universality of the laws of nature
In order to be able to describe the entire universe in each of its developmental stages on the basis of the laws of nature known to us, the assumption is essential that these laws of nature are universal and constant (independent of time). There are no observations in astronomy (looking back about 13.5 billion years) or paleogeology (4 billion years ago) to challenge this assumption.
From the assumed constancy and universality of the currently known laws of nature, it follows that the development of the universe as a whole can be described using the general theory of relativity and the processes taking place in it using the standard model of elementary particle physics . In the extreme case of large matter density and simultaneously large space-time curvature, the quantum field theories on which the standard model is based and the general theory of relativity are actually required for the description . However, the union encounters fundamental difficulties, so that at present the first few microseconds of the history of the universe cannot be consistently described.
The cosmological principle states that the universe looks the same at every point in space and also in all directions for great distances at the same time, and is also called (spatial) homogeneity ; the assumption that it looks the same in every direction is called (spatial) isotropy . A look at the starry sky with the naked eye immediately shows that the universe in the vicinity of the earth is not homogeneous and isotropic, because the distribution of the stars is irregular. On a larger scale, the stars form galaxies , some of which in turn form clusters of galaxies , but are otherwise distributed in a honeycomb-like structure made up of so-called filaments and voids . No structure is recognizable on an even larger scale. This and the high degree of isotropy of the cosmic background radiation justify the description of the universe as a whole using the cosmological principle.
If one applies the cosmological principle to the general theory of relativity, Einstein's field equations are simplified to the so-called Friedmann equations . These describe a homogeneous, isotropic universe. To solve the equations, one starts from the current state of the universe and follows the development backwards in time. The exact solution depends in particular on the measured values of the Hubble constant as well as various density parameters that describe the mass and energy content of the universe. One then finds that the universe used to be smaller ( expansion of the universe ); it was hotter and denser at the same time. Formally, the solution leads to a point in time at which the value of the scale factor disappears, i.e. the universe had no expansion and the temperature and density become infinitely large. This point in time is known as the “Big Bang”. It is a formal singularity of the solution to the Friedmann equations. However, this does not make any statement about the physical reality of such an initial singularity, since the equations of classical physics only have a limited range of validity and are no longer applicable if quantum effects play a role, as is assumed in the very early, hot and dense universe. A theory of quantum gravity is required to describe the evolution of the universe at very early times .
According to the Friedmann equations, the energy density of the universe was very high in its early phase. This means that the energies of the particles were also very high on average. The very early phase of the universe is therefore the subject of theories that cannot be verified by laboratory experiments.
The Planck era describes the period after the Big Bang up to the smallest physically meaningful time, the Planck time with about 10 −43 seconds. The temperature at this time corresponds to the Planck temperature , about 10 32 Kelvin. Until then, according to the scientists, there was only one fundamental force , the primal force . To date, there is no generally accepted theory for the Planck era. The M-theory and loop quantum gravity are considered possible candidates .
In cosmology it is generally assumed that the Planck era was followed by the GUT era or baryogenesis after a spontaneous symmetry break. The primal force split into the X-force or GUT-force and gravity. WELL stands for Grand Unified Theories to German Grand Unified Theory . This would unite the strong nuclear force , the weak nuclear force and the electromagnetic force . High-energy experiments at particle accelerators indicate that at an energy of around 2 · 10 16 GeV, the three mentioned forces can no longer be distinguished from one another. Above this energy there would only be one force called the GOOD force. This would be a state of higher symmetry. At energies below this value, this symmetry breaks and the three mentioned forces become visible. However, the necessary energy density cannot currently be achieved in laboratory experiments to adequately test such theories.
The inflation is temporally settled in the GUT era. During this so-called inflation, the universe expanded by a factor between 10 30 and 10 50 within 10 −35 to 10 −32 seconds . This faster than light expansion of the universe does not contradict the theory of relativity , since this only forbids a faster than light movement in space , but not a faster than light expansion of the space itself . According to the theory, the area that corresponds to the universe that can be observed today should have expanded from a diameter far below that of a proton to around 10 cm.
The exact details of the inflation are unknown, but the measurements of the temperature fluctuations of the cosmic background radiation by the WMAP satellite are a strong indication that an inflation with certain characteristics has taken place. The measurement results of the Planck space telescope could make it possible to gain more precise information about the inflationary epoch. The original inflation theory goes back to a paper by Alan Guth from 1981 and has been worked on by Andrei Dmitrijewitsch Linde and others since then. This theory uses one or more scalar fields called inflaton fields .
The cause of the end of inflation is also unclear. A possible explanation for this should be offered by slow-roll models in which the inflaton field reaches an energetic minimum and inflation therefore ends; an alternative is the GUT model already described, in which the end of inflation is explained by breaking the GUT symmetry.
A phase of inflation can explain several cosmological observations:
- the global homogeneity of the cosmos ( horizon problem ),
- the slight curvature of the room ( flatness problem ),
- the fact that no magnetic monopoles are observed,
- the large-scale structures in the cosmos such as galaxies and galaxy clusters ,
- the already mentioned spectrum of temperature fluctuations of cosmic background radiation.
However, the inflation model fails to explain the cosmological constant . Einstein's would not be constant, but rather dependent on time, an assumption that is used in quintessence models . Further models keep the cosmological constant constant.
Evolution of the universe
The time after the inflation and the speculative breaking of a possible GUT symmetry as well as the electroweak symmetry can be described with the known physical theories. The behavior of the universe from this phase onwards is relatively clear from observations and hardly differs in the various Big Bang models.
The formation of atomic nuclei in the early universe is called primordial nucleosynthesis. After the end of the inflation, i.e. after about 10 −30 s, the temperature dropped to 10 25 K. It formed quarks and anti-quarks, the building blocks of today's heavy particles (Baryogenese). However, the temperature was so high and the times between two particle collisions so short that stable protons or neutrons were not yet formed, but rather a so-called quark-gluon plasma was created from almost free particles. The time until stable hadrons are formed is also known as the quark era .
After 10 −6 s the temperature was 10 13 K. Quarks could no longer exist as free particles, but combined to form hadrons , i.e. H. Protons, neutrons and heavier relatives. After 10 −4 s the temperature had dropped to 10 12 K, so that no more proton-antiproton or neutron-antineutron pairs were formed. Most protons and neutrons were destroyed by collisions with their antiparticles - except for a small excess of one billionth. The density decreased to 10 13 g / cm 3 . As the temperature decreased, the heavier hadrons decayed, leaving protons and neutrons and their antiparticles. The constant conversion of protons into neutrons and vice versa also resulted in a large number of neutrinos . In this so-called hadron era , there were as many protons as neutrons, as they could be converted into one another at will due to the available energy. A temperature of 10 10 K was reached after 1 s . Below this temperature only neutrons could decay into protons, but neutrons could no longer be reproduced.
After 10 seconds at temperatures below 10 9 K, protons and neutrons remaining united by fusion to the first deuterium - nuclei . As long as these did not disintegrate again, they fused in pairs to form helium-4 nuclei. After about 3 minutes, the temperature and density of the matter had decreased so much that the nuclear fusion came to a standstill. The remaining free neutrons were not stable and decayed into protons and electrons over the next few minutes. In total, 25% helium-4 ( 4 He) and 0.001% deuterium as well as traces of helium-3 ( 3 He), lithium and beryllium were formed in the first three minutes . The remaining 75% were protons, the later hydrogen atomic nuclei.
All heavier elements were only created later inside stars. The temperature was still so high that the matter was present as plasma , a mixture of free atomic nuclei, protons and electrons, with thermal radiation in the X-ray range .
In addition to elementary particles and radiation, primordial magnetic fields were also created . This is attributed to the Harrison effect . It is believed that the plasma formed eddies in the hot and dense universe. The resulting friction on the very strong radiation field led to the generation of electrical currents that caused magnetic fields by induction .
Strongly coupled plasma
For neutrinos, which hardly interact with other particles, the density was low enough after 10 −4 s - they were no longer in thermal equilibrium with the other particles, that is, they were decoupled . A temperature of 10 10 K was reached after 1 s . Now electrons and positrons were also annihilated - with the exception of an excess of one billionth of electrons. This largely concluded the formation of the building blocks of matter from which the cosmos is still composed today. The universe was now filled with a strongly interacting plasma of electrons, photons ("light particles") and atomic nuclei, especially protons. There were also neutrinos that interacted with the hot plasma primarily through gravity. In addition, it is assumed within the framework of the cosmological standard model that there was a large amount of dark matter , which also only interacted with the plasma through gravity.
It took about 400,000 years for the temperature to drop sufficiently for stable atoms to form ( recombination epoch ) and for light to travel great distances without being absorbed. The mean free path of photons increased extremely, so the universe became transparent, more precisely its optical density decreased very rapidly. This decoupling of light took about 100,000 years. During this period of time, some regions of the universe had cooled down enough to be transparent, while other regions were still dominated by hot plasma. Since there were many more photons than protons in the universe at the time of decoupling, the temperature of the universe was significantly lower than the ionization energy of hydrogen , the Boltzmann constant being around , which corresponds to a temperature of around 4000 K. This means that the maximum radiation intensity at this time was in the visible spectrum. This radiation can still be measured today as cosmic background radiation . However, due to the cosmological redshift, it is now much longer-wave microwave radiation and corresponds to a temperature of 2.73 K.
The dynamics of the plasma are decisive for the development of temperature fluctuations in the background radiation and the formation of material structures. The behavior of the plasma-filled universe can be described in the context of cosmological perturbation theory using the Boltzmann equation . This explains certain basic characteristics of the spectrum of temperature fluctuations. In particular, there are pressure waves in the plasma, that is to say sound waves, so to speak , which cause certain characteristic peaks in the spectrum of temperature fluctuations. The fact that these peaks could be measured with great accuracy by the space probes WMAP and Planck is a supporting indication for these theories. The formation of large-scale structures is qualitatively explained by the fact that dark matter collects in places where the plasma is also denser and thus intensifies density imbalances so much that the matter finally collects almost exclusively in relatively small areas of the universe.
Radiation Era and Matter Era
The Friedmann equations are based on the matter model of the perfect fluid . In this model, matter is described by two state variables, namely energy density and pressure . The relationship between energy and pressure is described by an equation of state . The most important cases for the usual models of the universe are radiation with , massive particles, often referred to as “dust”, with, and a cosmological constant with . The dependence of the energy density on the scale factor is very different for the different types of matter , namely . The different time dependencies of radiation and massive particles can also be clearly understood; in the case of radiation, in addition to the decrease in the number density of the photons (due to the expansion of space), the wavelength of the individual photons increases due to the cosmological redshift . This ensures that the energy density of the radiation decreases faster than that of massive matter. Therefore, a universe that was initially dominated by radiation will be dominated by massive particles after a while, until a possible cosmological constant would prevail.
According to the Big Bang models, (electromagnetic) radiation made up the main part of the energy density in the cosmos after inflation. At a point in time around 70,000 years after the Big Bang, the energy densities of radiation and matter were the same, after which massive matter determined the dynamics of the universe. One speaks of the end of the radiation-dominated era and the beginning of the matter-dominated era.
Predictions of the Big Bang Models
The Big Bang models with the characteristics described above are the most recognized models for explaining the current state of the universe. The reason for this is that they make some key predictions that align well with the observed state of the universe. The most important predictions are the expansion of the universe, the cosmic background radiation and the element distribution, in particular the proportion of helium in the total mass of baryonic matter . The most important properties of the temperature fluctuations of the cosmic background radiation are also explained very successfully in the context of the Big Bang models using cosmological perturbation theory. The theory of temperature fluctuations also offers a model for the formation of large-scale structures, namely the filaments and voids that form the honeycomb structure described above.
Expansion of the universe
The expansion of the universe was first observed by Edwin Hubble in 1929 . He discovered that the distance of galaxies from the Milky Way and their redshift are proportional. The redshift is explained by the fact that the galaxies are moving away from the observer, Hubble's observation was the proportionality of distance and escape speed. At least since the work of Georges Lemaître in 1927 it was known that such a proportionality follows from the Friedmann equations, which also contain the Big Bang. This observation was the first confirmation of the Big Bang models. Today Hubble's law has been well confirmed by measurements on a large number of galaxies. However, an approximate proportionality, as predicted by the Friedmann equations for a universe with massive matter, only applies to comparatively close galaxies. However, very distant galaxies have escape speeds that are greater than is to be expected in a matter-dominated universe. This is interpreted as an indication of a cosmological constant or dark energy .
Frequency of elements
Most of the light atomic nuclei were formed in the first minutes of the universe during primordial nucleosynthesis . The description of this process in the context of the Big Bang model goes back to Ralph Alpher and George Gamow , who developed the Alpher-Bethe-Gamow theory . In particular, the mass fraction of helium of around 25% of ordinary matter (excluding dark matter) is predicted by the big bang models, in very good agreement with the observed frequency. By measuring the frequency of rarer nuclei such as deuterium , helium-3 and lithium -7, conclusions can be drawn about the density of ordinary matter in the universe. The measured frequencies of these elements are consistent with one another and with other measurements of matter density within the framework of the existing models.
Cosmic background radiation
The cosmic background radiation was predicted in 1948 by Ralph Alpher, George Gamow and Robert Herman . They then predicted different temperatures in the range of about 5 to 50 K. It was not until 1964 that Arno Penzias and Robert Woodrow Wilson identified the background radiation as a real effect for the first time, after several astronomers had previously mistaken measurements of the signal for antenna errors. The measured temperature was given as 3 K, today's measurements show a temperature of 2.725 K. The background radiation is isotropic to a very good approximation, that is, it has the same temperature and intensity in every direction. Deviations of 1% result from the Doppler effect due to the movement of the earth. The Milky Way can also be seen as a clear disruption.
Rainer K. Sachs and Arthur M. Wolfe predicted in 1967 that there would be very small temperature fluctuations in the background radiation. The effect they predicted was named the Sachs-Wolfe Effect in their honor . In 1993 the COBE satellite actually detected fluctuations of 0.001% in the temperature of the background radiation, with the WMAP satellite confirming this observation, as well as the Sachs-Wolfe effect. Other significant characteristics of the spectrum of temperature anisotropies are silk attenuation and baryonic acoustic oscillations .
Creation of large-scale structures
Due to the decoupling of the radiation, the matter came more strongly under the influence of gravity. On the basis of spatial density fluctuations, which may already have arisen in the inflationary phase due to quantum fluctuations , large-scale structures formed in the cosmos after 1 million years. The matter began to collapse in the spatial areas with a higher mass density as a result of gravitational instability and to form mass accumulations. So-called halos of dark matter were formed first , which acted as gravitational sinks in which the matter that was visible to us later collected. The baryonic matter, which is subject to the radiation pressure, did not have sufficient density to clump together into large-scale structures so early without the help of dark matter that the resulting temperature fluctuations can still be observed in the background radiation today. Without dark matter, the creation of large-scale structures such as the honeycomb structure made of voids and filaments, as well as the creation of smaller structures such as galaxies, would take much longer than the age of the universe, which results from the Big Bang models.
To investigate the properties of dark matter, an attempt was made to simulate the process of structure formation. Various scenarios were run through, and some could be excluded as completely unrealistic with the help of such simulations. So-called CDM scenarios seem realistic today , whereby this is the cosmological constant of Einstein's field equations , and CDM stands for cold dark matter. What kind of particles form dark matter is currently unknown.
The collapsing gas clouds had condensed so much that the first stars were forming. These were much more massive than our sun, so that they became very hot and created high pressures. As a result, heavier elements such as carbon, oxygen and iron were also created through nuclear fusion. Because of their large mass, the lifespan of these stars was relatively short at 3–10 million years; they exploded in a supernova . During the explosion, elements heavier than iron (e.g. uranium ) were formed by neutron capture and entered interstellar space. The explosion pressure condensed adjacent gas clouds, which could thus produce new stars more quickly. Since the gas clouds enriched with metals cooled down faster, stars with lower mass and smaller ones with weaker luminosity but with a longer lifespan were created.
The first globular clusters formed from these stars, and finally the first galaxies from their predecessors.
There are various models that match the Big Bang models from a time of around 10 −30 s and that aim to explain the very early universe without singularities. In some cases, such models can make additional predictions compared to the usual big bang models or deviate slightly in the predictions, provided that these deviations are not refuted by the measurement accuracy. Such models are mostly related to the theories of quantum gravity and loop quantum gravity (loop quantum gravity) as loop quantum cosmology .
Bran cosmology is a theory closely related to string theory and uses concepts from that theory. Bran cosmology models describe at least a five-dimensional space-time in which the four-dimensional space-time is embedded as a “brane” (the word is derived from “membrane”). The modern treatment of this theory was based on the Randall-Sundrum model developed in 1999 . In this a brane is supposed to model the observable universe. It provides an explanatory model for why gravity is much weaker than the other basic forces, but it does not describe any evolution of the universe. So it does not contain any expansion of the universe and therefore neither redshift nor background radiation. It is therefore not a realistic model of the observable universe.
A further developed model of branch cosmology is the cyclic ekpyrotic universe by Paul Steinhardt and Neil Turok , which is also based on string theory and was developed in 2002. In this model, two four-dimensional branes collide periodically in a five-dimensional space-time, each time creating a state like the one that prevailed in the very early universe according to the Big Bang model. In particular, they form an alternative to inflation theory, in that they make the same predictions within the framework of today's measurement accuracy. However, the ekpyrotic model makes different predictions about the polarization of the fluctuations in the background radiation, which means that future measurements can in principle falsify one of the two models.
Loop quantum cosmology
The loop quantum cosmology is a theory that has developed from loop quantum gravity (among others by Martin Bojowald ). Since the cosmological principle is assumed as an assumption in this theory, it has not yet been clarified to what extent it is compatible with loop quantum gravity itself. The Loop Quantum Cosmology provides an explanation for cosmic inflation and, with the Big Bounce, offers a cosmological model without Big Bang singularity. In this model, a previous universe collapses in a big crunch , but the effects of quantum gravity ensure that it does not collapse into a singularity, but only up to a maximum density. Then an expansion sets in again, from which today's universe emerges. This model is currently the subject of research and many questions are still unanswered. Among other things, it is not clear whether the history of the cyclical universe repeats itself identically or varies with each run. A further development of the model results in a cyclical universe that always alternately expands to a maximum extent and collapses to a minimum extent.
The theory of chaotic inflation was proposed by Andrei Linde in 1986 and is not tied to any particular quantum gravity theory. It says that the majority of the universe is constantly expanding in an inflationary manner and that inflation only comes to a standstill within various bubbles, so that a large number of sub-universes are formed. According to the model, the quantum fluctuations of the inflaton field ensure that most of the universe remains in the inflationary phase forever. Non-inflationary bubbles arise when the quantum fluctuations of the inflaton field become smaller locally. Although the probability of the formation of these bubbles is very high, the high speed of inflation ensures that they become very much smaller compared to the rest of the universe, so that they only collide very rarely and the majority of the universe is characterized by eternal inflation.
The different sub-universes can contain different values of the natural constants and thus different physical laws if there are several stable states of the field. The theory is sometimes also understood as a multiverse theory (for example Alexander Vilenkin ), as there are many sub-universes that can never come into contact with each other. The inflationary multiverse is also called quantum foam because its properties do not match the observable universe. According to the theory, it contains neither matter nor radiation, only the inflaton field.
In antiquity, the pre-Socratic natural philosophers, which are now lost, had developed ideas of a big bang, the main features of which were already close to modern knowledge. In particular, the teachings on the creation of the universe by Anaxagoras in the 5th century BC BC, according to which the universe is expanding, are often associated with the Big Bang in modern research .
The Belgian theologian and physicist Georges Lemaître is considered to be the founder of the Big Bang theory . The English name Big Bang (literally 'Big Bang') was coined by Fred Hoyle . Hoyle advocated the steady state theory and wanted to use the words Big Bang to make the image of an expanding universe that appears to emerge from nowhere appear implausible. The steady state theory lost support in the 1960s when the big bang theory was increasingly confirmed by astronomical observations.
The general theory of relativity published by Albert Einstein in 1915 forms the prerequisite for modern cosmology and thus also for the Big Bang models . In 1922, Alexander Friedmann laid the foundation for the Big Bang models with his description of the expanding universe. Although Einstein acknowledged that his model was compatible with the field equations , Friedmann's work was initially hardly discussed, as no astronomical observations indicated an expansion of the universe and therefore static cosmological models were preferred, including by Einstein himself. Lemaître developed Friedmann's model in 1927 independently of this again and led it further to a first big bang theory, according to which the universe emerged from a single particle, the "primordial atom". As a result of the expansion of the universe, he already derived a proportionality of the distance and the escape speed of stellar objects. However, this work also received little attention.
In 1929, Edwin Hubble discovered through distance measurements on Cepheids in galaxies outside the Milky Way that the redshift of the galaxies is proportional to their distance. He explained this finding, which is now called Hubble's law , by the Doppler effect as a result of an expansion of the universe. Hubble thus confirmed Lemaître's prediction, although he was not aware of it and does not refer to it in his writings. In 1935, Howard P. Robertson and Arthur Geoffrey Walker finally proved that the Friedmann-Lemaître-Robertson-Walker metrics, regardless of the matter model, are the only metrics that are compatible with the cosmological principle.
In 1948 Ralph Alpher , George Gamow and Robert Herman developed a theory of the creation of the cosmos from a hot initial state. As part of this theory, they predicted both the abundance of helium in the early universe and the existence of cosmic background radiation with a black body spectrum . For the current temperature of the background radiation, they gave various estimates in the range from 5 K to 50 K. Arno Penzias and Robert Woodrow Wilson unintentionally discovered cosmic microwave background radiation in 1964 . Since they only measured on two frequencies, they could not determine that the radiation has a blackbody spectrum. This was confirmed by further measurements in the following years and the temperature was measured at 3 K. In 1967 Rainer K. Sachs and Arthur M. Wolfe predicted temperature fluctuations in cosmic background radiation. This effect is named after them as the Sachs-Wolfe effect .
Stephen Hawking and Roger Penrose showed mathematically from 1965 to 1969 that the still doubted ultra-dense states at the beginning of time necessarily result under the assumptions "validity of general relativity" and "expanding universe".
To explain the extremely homogeneous and isotropic initial state of the observable universe, which is inferred from the isotropy of the cosmic background radiation, Roger Penrose proposed the Weyl curvature hypothesis in 1979 . This hypothesis also provides an explanation for the origin of the second law of thermodynamics . As a competing hypothesis to explain the homogeneity and isotropy of the early universe and to solve the horizon problem, Alan Guth developed the theory of the inflationary universe in 1981, which postulates a phase of very rapid expansion in the early phase of the universe. The theory of the inflationary universe was later developed further by Andrei Linde and others and was finally able to establish itself as an explanatory model.
Valerie de Lapparent, Margaret Geller and John Huchra discovered in 1986 the arrangement of clusters of galaxies in wall-like structures, in turn, large-scale, bubble-like voids ( voids enclose). The cosmic background radiation was measured with considerable accuracy by the satellites COBE (1989–1993), WMAP (2001–2010) and Planck (2009–2013). The fluctuations in the background radiation were discovered and their spectrum measured, confirming the prediction of Sachs and Wolfe. The measurement results of these satellites in connection with distance measurements allowed a more precise determination of cosmological parameters, which give indications of an accelerated expanding universe.
“Before” the Big Bang
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- What is the big bang? from the alpha-Centauri television series(approx. 15 minutes). First broadcast on Feb 27, 2000.
- What was before the Big Bang? from the alpha-Centauri television series(approx. 15 minutes). First broadcast on Oct 14, 2001.
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- Helge Kragh : Big Bang Cosmology . In: Hetherington 2014, see Bibliography, p. 40.
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- David Spergel et al .: First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters . In: ApJS . Volume 148, 2003, p. 175