10 BIG BANG NUCLEOSYNTHESIS  

 

10.1 General 

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Big Bang Nucleosynthesis is the production of nuclei other than those of the lightest isotope of hydrogen (hydrogen-1, 1H, having a single proton as a nucleus) during the early phases of the Universe.  [1]

Primordial nucleosynthesis is believed by most cosmologists to have taken place in the interval from roughly 10 seconds to 20 minutes after the Big Bang,[2]  and is calculated to be responsible for the formation of most of the universe's helium as the isotope helium-4 (⁴He)

 

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along with small amounts of the hydrogen isotope deuterium (²H or D), the helium isotope helium-3 (³He), and a very small amount of the lithium isotope lithium-7 (⁷Li).

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In addition to these stable nuclei, two unstable or radioactive isotopes were also produced: the heavy hydrogen isotope tritium (3H or T); and the beryllium isotope beryllium-7 (7Be); but these unstable isotopes later decayed into 3He and 7Li, respectively, as above.

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Essentially all of the elements that are heavier than lithium were created much later, by stellar nucleosynthesis in evolving and exploding stars.

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10.2 Characteristics 

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There are several important characteristics of Big Bang nucleosynthesis (BBN):

• The initial conditions (neutron–proton ratio) were set in the first second after the Big Bang.

• The universe was very close to homogeneous at this time, and strongly radiation-dominated.

• The fusion of nuclei occurred between roughly 10 seconds to 20 minutes after the Big Bang; this corresponds to the temperature range when the universe was cool enough for deuterium to survive, but hot and dense enough for fusion reactions to occur at a significant rate. [[2]]

• It was widespread, encompassing the entire observable universe.

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The key parameter which allows one to calculate the effects of Big Bang nucleosynthesis is the baryon/photon number ratio, which is a small number of order 6 ×10⁻¹⁰. This parameter corresponds to the baryon density and controls the rate at which nucleons collide and react; from this it is possible to calculate element abundances after nucleosynthesis ends. Although the baryon per photon ratio is important in determining element abundances, the precise value makes little difference to the overall picture.

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Without major changes to the Big Bang theory itself, BBN will result in mass abundances of about 75% of hydrogen-1, about 25% helium-4, about 0.01% of deuterium and helium-3, trace amounts (on the order of 10⁻¹⁰) of lithium, and negligible heavier elements. That the observed abundances in the universe are generally consistent with these abundance numbers is considered strong evidence for the Big Bang theory.

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In this field, for historical reasons it is customary to quote the helium-4 fraction by mass, symbol Y, so that 25% helium-4 means that helium-4 atoms account for 25% of the mass, but less than 8% of the nuclei would be helium-4 nuclei. Other (trace) nuclei are usually expressed as number ratios to hydrogen. The first detailed calculations of the primordial isotopic abundances came in 1966 [3] [4] and have been refined over the years using updated estimates of the input nuclear reaction rates. The first systematic Monte Carlo study of how nuclear reaction rate uncertainties impact isotope predictions, over the relevant temperature range, was carried out in 1993. [5]

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10.3 Important parameters

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The creation of light elements during BBN was dependent on a number of parameters; among those was the neutron–proton ratio (calculable from Standard Model physics) and the baryon-photon ratio.

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10.3.1 Neutron–proton ratio

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The neutron–proton ratio was set by Standard Model physics before the nucleosynthesis era, essentially within the first 1-second after the Big Bang. Neutrons can react with positrons or electron neutrinos to create protons and other products in one of the following reactions:

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At times much earlier than 1 sec, these reactions were fast and maintained the n/p ratio close to 1:1. As the temperature dropped, the equilibrium shifted in favour of protons due to their slightly lower mass, and the n/p ratio smoothly decreased. These reactions continued until the decreasing temperature and density caused the reactions to become too slow, which occurred at about T = 0.7 MeV (time around 1 second) and is called the freeze out temperature.

 

At freeze out, the neutron–proton ratio was about 1/6. However, free neutrons are unstable with a mean life of 880 sec; some neutrons decayed in the next few minutes before fusing into any nucleus, so the ratio of total neutrons to protons after nucleosynthesis ends is about 1/7. Almost all neutrons that fused instead of decaying ended up combined into helium-4, due to the fact that helium-4 has the highest binding energy per nucleon among light elements. This predicts that about 8% of all atoms should be helium-4, leading to a mass fraction of helium-4 of about 25%, which is in line with observations. Small traces of deuterium and helium-3 remained as there was insufficient time and density for them to react and form helium-4 [6]

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10.3.2 Baryon–photon ratio

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The baryon–photon ratio, η, is the key parameter determining the abundances of light elements after nucleosynthesis ends. Baryons and light elements can fuse in the following main reactions:

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along with some other low-probability reactions leading to 7Li or 7Be. (An important feature is that there are no stable nuclei with mass 5 or 8, which implies that reactions adding one baryon to 4He, or fusing two 4He, do not occur).

Most fusion chains during BBN ultimately terminate in 4He (helium-4), while "incomplete" reaction chains lead to small amounts of left-over 2H or 3He; the amount of these decreases with increasing baryon-photon ratio. That is, the larger the baryon-photon ratio the more reactions there will be and the more efficiently deuterium will be eventually transformed into helium-4. This result makes deuterium a very useful tool in measuring the baryon-to-photon ratio.

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10.3.3 Sequence

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Big Bang nucleosynthesis began roughly about 20 seconds after the big bang, when the universe had cooled sufficiently to allow deuterium nuclei to survive disruption by high-energy photons. (Note that the neutron–proton freeze-out time was earlier). This time is essentially independent of dark matter content, since the universe was highly radiation dominated until much later, and this dominant component controls the temperature/time relation. At this time there were about six protons for every neutron, but a small fraction of the neutrons decay before fusing in the next few hundred seconds, so at the end of nucleosynthesis there are about seven protons to every neutron, and almost all the neutrons are in Helium-4 nuclei. [7]

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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, and proceeds independently of what happened before.

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As the universe expands, it cools. Free neutrons 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. Before nucleosynthesis began, the temperature was high enough for many photons to have energy greater than the binding energy of deuterium; therefore any deuterium that was formed was immediately destroyed (a situation known as the "deuterium bottleneck"). Hence, the formation of helium-4 is delayed until the universe became cool enough for deuterium to survive (at about T = 0.1 MeV); after which there was a sudden burst of element formation. However, very shortly thereafter, around twenty minutes after the Big Bang, the temperature and density became too low for any significant fusion to occur.

 

• The first step in forming helium-4 was the creation of deuterium (a heavy isotope of hydrogen). A free neutron and a proton combined to form a deuterium nucleus, releasing a neutrino in the process:

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n + p → D + ν

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• Once a significant amount of deuterium was formed, it could interact with free protons and neutrons, resulting in the formation of helium-3:

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D + p → He-3 + γ

or

D + n → He-3 + ν

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• Helium-3 nuclei could then interact with either a deuterium nucleus or another helium-3 nucleus to form helium-4:

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He-3 + D → He-4 + p

or

He-3 + He-3 → He-4 + 2p

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At this point, the elemental abundances were nearly fixed, and the only changes were the result of the radioactive decay of the two major unstable products of BBN, tritium and beryllium-7. [8]

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