Big Bang nucleosynthesis

Big Bang nucleosynthesis

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In physical cosmology
Physical cosmology
Physical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...

, Big Bang nucleosynthesis (or primordial nucleosynthesis, abbreviated BBN) refers to the production of nuclei other than those of H-1 (i.e. the normal, light isotope
Isotope
Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...

 of hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

, whose nuclei consist of a single proton each) during the early phases of the universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

. Primordial nucleosynthesis
Nucleosynthesis
Nucleosynthesis is the process of creating new atomic nuclei from pre-existing nucleons . It is thought that the primordial nucleons themselves were formed from the quark–gluon plasma from the Big Bang as it cooled below two trillion degrees...

 took place just a few moments after the Big Bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

 and is believed to be responsible for the formation of a heavier isotope
Isotope
Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...

 of hydrogen known as deuterium
Deuterium
Deuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...

 (H-2 or D), the helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...

 isotopes He-3 and He-4, and the lithium
Lithium
Lithium is a soft, silver-white metal that belongs to the alkali metal group of chemical elements. It is represented by the symbol Li, and it has the atomic number 3. Under standard conditions it is the lightest metal and the least dense solid element. Like all alkali metals, lithium is highly...

 isotopes Li-6 and Li-7. In addition to these stable nuclei some unstable, or radioactive
Radionuclide
A radionuclide is an atom with an unstable nucleus, which is a nucleus characterized by excess energy available to be imparted either to a newly created radiation particle within the nucleus or to an atomic electron. The radionuclide, in this process, undergoes radioactive decay, and emits gamma...

, isotopes were also produced during primordial nucleosynthesis: tritium
Tritium
Tritium is a radioactive isotope of hydrogen. The nucleus of tritium contains one proton and two neutrons, whereas the nucleus of protium contains one proton and no neutrons...

 or H-3; beryllium-7
Beryllium
Beryllium is the chemical element with the symbol Be and atomic number 4. It is a divalent element which occurs naturally only in combination with other elements in minerals. Notable gemstones which contain beryllium include beryl and chrysoberyl...

 (Be-7), and beryllium-8 (Be-8). These unstable isotopes either decayed or fused with other nuclei to make one of the stable isotopes.

Characteristics of Big Bang nucleosynthesis


There are two important characteristics of Big Bang nucleosynthesis (BBN):
  • It lasted for only about seventeen minutes (during the period from 3 to about 20 minutes from the beginning of space expansion
    Metric expansion of space
    The metric expansion of space is the increase of distance between distant parts of the universe with time. It is an intrinsic expansion—that is, it is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space...



after that, the temperature and density of the universe fell below that which is required for nuclear fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...

. The brevity of BBN is important because it prevented elements heavier than beryllium
Beryllium
Beryllium is the chemical element with the symbol Be and atomic number 4. It is a divalent element which occurs naturally only in combination with other elements in minerals. Notable gemstones which contain beryllium include beryl and chrysoberyl...

 from forming while at the same time allowing unburned light elements, such as deuterium
Deuterium
Deuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...

, to exist.
  • It was widespread, encompassing the entire observable universe
    Observable universe
    In Big Bang cosmology, the observable universe consists of the galaxies and other matter that we can in principle observe from Earth in the present day, because light from those objects has had time to reach us since the beginning of the cosmological expansion...

    .


The key parameter which allows one to calculate the effects of BBN is the number of photons per baryon
Baryon
A baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quark-based particles...

. This parameter corresponds to the temperature and density of the early universe and allows one to determine the conditions under which nuclear fusion occurs. From this we can derive elemental abundances. Although the baryon per photon ratio is important in determining elemental abundances, the precise value makes little difference to the overall picture. Without major changes to the Big Bang theory itself, BBN will result in mass abundances of about 75% of H-1, about 25% helium-4
Helium-4
Helium-4 is a non-radioactive isotope of helium. It is by far the most abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on earth. Its nucleus is the same as an alpha particle, consisting of two protons and two neutrons. Alpha decay of heavy...

, about 0.01% of deuterium, trace (on the order of 10−10) amounts of lithium and beryllium, and no other heavy elements. (Traces of boron
Boron
Boron is the chemical element with atomic number 5 and the chemical symbol B. Boron is a metalloid. Because boron is not produced by stellar nucleosynthesis, it is a low-abundance element in both the solar system and the Earth's crust. However, boron is concentrated on Earth by the...

 have been found in some old stars, giving rise to the question that some boron, not really predicted by the theory, might have been produced in the Big Bang. The question is not presently resolved.) That the observed abundances in the universe are generally consistent with these abundance numbers is considered strong evidence for the Big Bang theory.

In this field it is customary to quote percentages by mass, so that 25% helium-4 means that helium-4 atoms account for 25% of the mass, but only about 8% of the atoms would be helium-4 atoms.

Sequence of Big Bang nucleosynthesis


Big Bang nucleosynthesis begins about three minutes after the Big Bang, when the universe has cooled down sufficiently to form stable proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

s and neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

s, after baryogenesis
Baryogenesis
In physical cosmology, baryogenesis is the generic term for hypothetical physical processes that produced an asymmetry between baryons and antibaryons in the very early universe, resulting in the substantial amounts of residual matter that make up the universe today.Baryogenesis theories employ...

. The relative abundances of these particles follow from simple thermodynamical arguments, combined with the way that the mean temperature of the universe changes over time (if the reactions needed to reach the thermodynamically favoured equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...

 values are too slow compared to the temperature change brought about by the expansion, abundances will remain at some specific non-equilibrium value). Combining thermodynamics and the changes brought about by cosmic expansion, one can calculate the fraction of protons and neutrons based on the temperature at this point. The answer is that there are about seven protons for every neutron at the beginning of nucleogenesis, a ratio that would remain stable even after nucleogenesis is over. This fraction is in favour of protons initially primarily because lower mass of the proton favors their production. Free neutrons also decay to protons with a half-life of about 15 minutes, and this time-scale is too long to affect the number of neutrons over the period in which BBN took place, primarily because most of the free neutrons had already been absorbed in the first 3 minutes of nucleogenesis—a time too short for a significant fraction of them to decay to protons.

One feature of BBN is that the physical laws and constants that govern the behavior of matter at these energies are very well understood, and hence BBN lacks some of the speculative uncertainties that characterize earlier periods in the life of the universe. Another feature is that the process of nucleosynthesis is determined by conditions at the start of this phase of the life of the universe, making what happens before irrelevant.

As the universe expands, it cools. Free neutrons and protons are less stable than helium nuclei, and the protons and neutrons have a strong tendency to form helium-4. However, forming helium-4 requires the intermediate step of forming deuterium. At the time at which nucleosynthesis occurs, the temperature is high enough for the mean energy per particle to be greater than the binding energy of deuterium; therefore any deuterium that is formed is immediately destroyed (a situation known as the deuterium bottleneck). Hence, the formation of helium-4 is delayed until the universe becomes cool enough to form deuterium (at about T = 0.1 MeV), when there is a sudden burst of element formation. Shortly thereafter, at twenty minutes after the Big Bang, the universe becomes too cool for any nuclear fusion to occur. At this point, the elemental abundances are fixed, and only change as some of the radioactive products of BBN (such as tritium
Tritium
Tritium is a radioactive isotope of hydrogen. The nucleus of tritium contains one proton and two neutrons, whereas the nucleus of protium contains one proton and no neutrons...

) decay.

History of Big Bang nucleosynthesis theory


The history of Big Bang nucleosynthesis began with the calculations of Ralph Alpher and George Gamow
George Gamow
George Gamow , born Georgiy Antonovich Gamov , was a Russian-born theoretical physicist and cosmologist. He discovered alpha decay via quantum tunneling and worked on radioactive decay of the atomic nucleus, star formation, stellar nucleosynthesis, Big Bang nucleosynthesis, cosmic microwave...

 in the 1940s. Alpher and Gamow would publish the seminal Alpher-Bethe-Gamow paper
Alpher-Bethe-Gamow paper
In physical cosmology, the Alpher–Bethe–Gamow paper, or αβγ paper, was created by Ralph Alpher, then a physics PhD student, and his advisor George Gamow. The work, which would become the subject of Alpher's PhD dissertation, argued that the Big Bang would create hydrogen, helium and heavier...

 outlining the theory of light-element production in the early universe.

During the 1970s, there was a major puzzle in that the density of baryons as calculated by Big Bang nucleosynthesis was much less than the observed mass of the universe based on calculations of the expansion rate. This puzzle was resolved in large part by postulating the existence of dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...

.

Heavy elements


Big Bang nucleosynthesis produced no elements heavier than beryllium
Beryllium
Beryllium is the chemical element with the symbol Be and atomic number 4. It is a divalent element which occurs naturally only in combination with other elements in minerals. Notable gemstones which contain beryllium include beryl and chrysoberyl...

, due to a bottleneck: the absence of a stable nucleus with 8 or 5 nucleon
Nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...

s. In stars
Stellar nucleosynthesis
Stellar nucleosynthesis is the collective term for the nuclear reactions taking place in stars to build the nuclei of the elements heavier than hydrogen. Some small quantity of these reactions also occur on the stellar surface under various circumstances...

, the bottleneck is passed by triple collisions of helium-4 nuclei, producing carbon
Carbon
Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

 (the triple-alpha process
Triple-alpha process
The triple alpha process is a set of nuclear fusion reactions by which three helium-4 nuclei are transformed into carbon.Older stars start to accumulate helium produced by the proton–proton chain reaction and the carbon–nitrogen–oxygen cycle in their cores...

). However, this process is very slow, taking tens of thousands of years to convert a significant amount of helium to carbon in stars, and therefore it made a negligible contribution in the minutes following the Big Bang.

Helium-4



Big Bang nucleosynthesis predicts a primordial abundance of about 25% helium-4 by mass, irrespective of the initial conditions of the universe. As long as the universe was hot enough for protons and neutrons to transform into each other easily, their ratio, determined solely by their relative masses, was about 1 neutron to 7 protons (allowing for some decay of neutrons into protons). Once it was cool enough, the neutrons quickly bound with an equal number of protons to form helium-4. Helium-4 is very stable and neither decays nor combines easily to form heavier nuclei. So out of every 16 nucleons (2 neutrons and 14 protons), 4 of these (25%) combined into one helium-4 nucleus. One analogy is to think of helium-4 as ash, and the amount of ash that one forms when one completely burns a piece of wood is insensitive to how one burns it.

The helium-4 abundance is important because there is far more helium-4 in the universe than can be explained by stellar nucleosynthesis
Stellar nucleosynthesis
Stellar nucleosynthesis is the collective term for the nuclear reactions taking place in stars to build the nuclei of the elements heavier than hydrogen. Some small quantity of these reactions also occur on the stellar surface under various circumstances...

. In addition, it provides an important test for the Big Bang theory. If the observed helium abundance is much different from 25%, then this would pose a serious challenge to the theory. This would particularly be the case if the early helium-4 abundance was much smaller than 25% because it is hard to destroy helium-4. For a few years during the mid-1990s, observations suggested that this might be the case, causing astrophysicists to talk about a Big Bang nucleosynthetic crisis, but further observations were consistent with the Big Bang theory.

Deuterium



Deuterium is in some ways the opposite of helium-4 in that while helium-4 is very stable and very difficult to destroy, deuterium is only marginally stable and easy to destroy. Because helium-4 is very stable, there is a strong tendency on the part of two deuterium nuclei to combine to form helium-4. The only reason BBN does not convert all of the deuterium in the universe to helium-4 is that the expansion of the universe cooled the universe and cut this conversion short before it could be completed. One consequence of this is that unlike helium-4, the amount of deuterium is very sensitive to initial conditions. The denser the universe is, the more deuterium gets converted to helium-4 before time runs out, and the less deuterium remains.

There are no known post-Big Bang processes which would produce significant amounts of deuterium. Hence observations about deuterium abundance suggest that the universe is not infinitely old, which is in accordance with the Big Bang theory.

During the 1970s, there were major efforts to find processes that could produce deuterium, which turned out to be a way of producing isotopes other than deuterium. The problem was that while the concentration of deuterium in the universe is consistent with the Big Bang model as a whole, it is too high to be consistent with a model that presumes that most of the universe consists of proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

s and neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

s. If one assumes that all of the universe consists of protons and neutrons, the density of the universe is such that much of the currently observed deuterium would have been burned into helium-4.

This inconsistency between observations of deuterium and observations of the expansion rate of the universe led to a large effort to find processes that could produce deuterium. After a decade of effort, the consensus was that these processes are unlikely, and the standard explanation now used for the abundance of deuterium is that the universe does not consist mostly of baryons, and that non-baryonic matter (also known as dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...

) makes up most of the matter mass of the universe. This explanation is also consistent with calculations that show that a universe made mostly of protons and neutrons would be far more clumpy than is observed.

It is very hard to come up with another process that would produce deuterium via nuclear fusion. What this process would require is that the temperature be hot enough to produce deuterium, but not hot enough to produce helium-4, and that this process immediately cools down to non-nuclear temperatures after no more than a few minutes. Also, it is necessary for the deuterium to be swept away before it reoccurs.

Producing deuterium by fission is also difficult. The problem here again is that deuterium is very subject to nuclear processes, and that collisions between atomic nuclei are likely to result either in the absorption of the nuclei, or in the release of free neutrons or alpha particles. During the 1970s, attempts were made to use cosmic ray spallation
Cosmic ray spallation
Cosmic ray spallation is a form of naturally occurring nuclear fission and nucleosynthesis. It refers to the formation of elements from the impact of cosmic rays on an object. Cosmic rays are highly energetic charged particles from outside of Earth ranging from protons, alpha particles, and nuclei...

 to produce deuterium. These attempts failed to produce deuterium, but did unexpectedly produce other light elements.

Observational Tests and Status of Big Bang nucleosynthesis


The theory of BBN gives a detailed mathematical description of the production of the light "elements" deuterium, helium-3, helium-4, and lithium-7. Specifically, the theory yields precise quantitative predictions for the mixture of these elements, that is, the primordial abundances.

In order to test these predictions, it is necessary to reconstruct the primordial abundances as faithfully as possible, for instance by observing astronomical objects in which very little stellar nucleosynthesis
Stellar nucleosynthesis
Stellar nucleosynthesis is the collective term for the nuclear reactions taking place in stars to build the nuclei of the elements heavier than hydrogen. Some small quantity of these reactions also occur on the stellar surface under various circumstances...

 has taken place (such as certain dwarf galaxies
Dwarf galaxy
A dwarf galaxy is a small galaxy composed of up to several billion stars, a small number compared to our own Milky Way's 200-400 billion stars...

) or by observing objects that are very far away, and thus can be seen in a very early stage of their evolution (such as distant quasar
Quasar
A quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...

s).

As noted above, in the standard picture of BBN, all of the light element abundances depend on the amount of ordinary matter (baryon
Baryon
A baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quark-based particles...

s) relative to radiation (photons). Since the universe is homogeneous
Cosmological Principle
In modern physical cosmology, the cosmological principle is the working assumption that observers on Earth do not occupy an unusual or privileged location within the universe as a whole, judged as observers of the physical phenomena produced by uniform and universal laws of physics...

, it has one unique value of the baryon-to-photon ratio. For a long time, this meant that to test BBN theory against observations one had to ask: can all of the light element observations be explained with a single value of the baryon-to-photon ratio? Or more precisely, allowing for the finite precision of both the predictions and the observations, one asks: is there some range of baryon-to-photon values which can account for all of the observations?

More recently, the question has changed: Precision observations of the cosmic microwave background radiation
Cosmic microwave background radiation
In cosmology, cosmic microwave background radiation is thermal radiation filling the observable universe almost uniformly....

 with the Wilkinson Microwave Anisotropy Probe
Wilkinson Microwave Anisotropy Probe
The Wilkinson Microwave Anisotropy Probe — also known as the Microwave Anisotropy Probe , and Explorer 80 — is a spacecraft which measures differences in the temperature of the Big Bang's remnant radiant heat — the Cosmic Microwave Background Radiation — across the full sky. Headed by Professor...

 (WMAP) give an independent value for the baryon-to-photon ratio. Using this value, are the BBN predictions for the abundances of light elements in agreement with the observations?

The present measurement of helium-4 indicates good agreement, and yet better agreement for helium-3. But for lithium-7, there is a significant discrepancy between BBN and WMAP, and the abundance derived from Population II stars. The discrepancy is a factor of 2.4―4.3. and is considered a problem for the original models, that have resulted in revised calculations of the standard BBN based on new nuclear data, and to various reevaluation proposals for primordial proton-proton nuclear reactions, especially the intensities of 7Be(n,p)7Li versus 7Be(d,p)8Be.

Non-standard Big Bang nucleosynthesis


In addition to the standard BBN scenario there are numerous non-standard BBN scenarios. These should not be confused with non-standard cosmology
Non-standard cosmology
A non-standard cosmology is any physical cosmological model of the universe that has been, or still is, proposed as an alternative to the big bang model of standard physical cosmology...

: a non-standard BBN scenario assumes that the Big Bang occurred, but inserts additional physics in order to see how this affects elemental abundances. These pieces of additional physics include relaxing or removing the assumption of homogeneity, or inserting new particles such as massive neutrino
Neutrino
A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...

s.

There have been, and continue to be, various reasons for researching non-standard BBN. The first, which is largely of historical interest, is to resolve inconsistencies between BBN predictions and observations. This has proved to be of limited usefulness in that the inconsistencies were resolved by better observations, and in most cases trying to change BBN resulted in abundances that were more inconsistent with observations rather than less. The second, which is largely the focus of non-standard BBN in the early 21st century, is to use BBN to place limits on unknown or speculative physics. For example, standard BBN assumes that no exotic hypothetical particles were involved in BBN. One can insert a hypothetical particle (such as a massive neutrino) and see what has to happen before BBN predicts abundances which are very different from observations. This has been usefully done to put limits on the mass of a stable tau neutrino.

See also



  • Nucleosynthesis
    Nucleosynthesis
    Nucleosynthesis is the process of creating new atomic nuclei from pre-existing nucleons . It is thought that the primordial nucleons themselves were formed from the quark–gluon plasma from the Big Bang as it cooled below two trillion degrees...

  • Stellar nucleosynthesis
    Stellar nucleosynthesis
    Stellar nucleosynthesis is the collective term for the nuclear reactions taking place in stars to build the nuclei of the elements heavier than hydrogen. Some small quantity of these reactions also occur on the stellar surface under various circumstances...

  • Ultimate fate of the Universe
    Ultimate fate of the universe
    The ultimate fate of the universe is a topic in physical cosmology. Many possible fates are predicted by rival scientific theories, including futures of both finite and infinite duration....


For a general audience


Technical articles

Report-no: FERMILAB-Pub-00-239-A
  • Jedamzik, Karsten, "Non-Standard Big Bang Nucleosynthesis Scenarios". Max-Planck-Institut für Astrophysik, Garching.
  • Steigman, Gary, Primordial Nucleosynthesis: Successes And Challenges ; Forensic Cosmology: Probing Baryons and Neutrinos With BBN and the CBR ; and Big Bang Nucleosynthesis: Probing the First 20 Minutes
  • R. A. Alpher, H. A. Bethe, G. Gamow, The Origin of Chemical Elements, Physical Review 73 (1948), 803. The so-called αβγ paper
    Alpher-Bethe-Gamow paper
    In physical cosmology, the Alpher–Bethe–Gamow paper, or αβγ paper, was created by Ralph Alpher, then a physics PhD student, and his advisor George Gamow. The work, which would become the subject of Alpher's PhD dissertation, argued that the Big Bang would create hydrogen, helium and heavier...

    , in which Alpher and Gamow suggested that the light elements were created by hydrogen ions capturing neutrons in the hot, dense early universe. Bethe's name was added for symmetry
  • G. Gamow, The Origin of Elements and the Separation of Galaxies, Physical Review 74 (1948), 505. These two 1948 papers of Gamow laid the foundation for our present understanding of big-bang nucleosynthesis
  • G. Gamow, Nature 162 (1948), 680
  • R. A. Alpher, "A Neutron-Capture Theory of the Formation and Relative Abundance of the Elements," Physical Review 74 (1948), 1737
  • R. A. Alpher and R. Herman, "On the Relative Abundance of the Elements," Physical Review 74 (1948), 1577. This paper contains the first estimate of the present temperature of the universe
  • R. A. Alpher, R. Herman, and G. Gamow Nature 162 (1948), 774
  • Java Big Bang element abundance calculator