Richard H. Cyburt

PRIMORDIAL NUCLEOSYNTHESIS IN THE NEW AGE OF COSMOLOGY: DETERMINING UNCERTAINTIES, EXAMINING CONCORDANCE, AND PROBING NEW PHYSICS

Chapter 1

Overview -- An Introduction to Cosmology -- Primordial Nucleosynthesis -- Cosmic Microwave Background -- Bibliography

Primordial Nucleosynthesis

Big Bang Nucleosynthesis (BBN) refers to an epoch in the early universe when the lightest elements were synthesized (i.e. D, 3He, 4He, & 7Li). For reviews of BBN theory see Walker et al. (1991) [25], Sarkar (1996) [26], Olive, Steigman and Walker (2000) [27] and Fields and Sarkar (2002) [28]. At a time of about 1 second after the big bang, the universe had expanded and cooled to a temperature of about 10 billion Kelvin ( 1 MeV). At this time, the primeval soup consisted mainly of relativistic particles, like photons, neutrinos, and electrons and positrons. Normal matter or baryons consisted only a tiny fraction of the universe, about 1 baryon for every billion photons. We quantify this fraction with the baryon-to-photon ratio,

Standard primordial nucleosynthesis assumes baryon homogeneity and the Standard Model of particle physics with N = 3. Thus is the only free parameter, being related to the baryon density (B / Bh2 = 3:650 107´, where H = 100h km s¡1 Mpc¡1). The baryons are primarily protons and neutrons at this time. All of the interactions between these particles were so rapid that this plasma maintained thermal and chemical equilibrium. Dark matter was also present at this time, having similar densities as baryons. However its interactions are slow compared with the expansion rate and thus dark matter does not exist in thermal equilibrium with the rest of the plasma. The addition of dark matter{baryon interactions can affect the light element predictions, see Cyburt, Fields, Pavlidou and Wandelt [29].

As the universe continued to expand and cool, some of the interactions started slowing down. In particular, the weak interactions keeping the 3 species of neutrinos in thermal equilibrium and keeping the neutrons and protons in chemical equilibrium, become slow relative to the expansion rate. The neutrinos decouple from the plasma, adiabatically cooling with the expansion of the universe. The neutron-to-proton ratio effectively freezes out, with n-p inter-conversion no longer energetically favorable. This ratio stays roughly constant, with the exception of occasional neutron decay, until the start of nucleosynthesis.

After the universe has cooled below 1 MeV, it is no longer favorable for photons to pair produce electrons and positrons. Pair production effectively stops, and all that remains is electron/positron annihilation into photons. This net production of photons heats the particles that are still in thermal contact to a higher temperature than the neutrinos. What's left are still dominantly relativistic particles, consisting of photons and neutrinos (now different temperatures), with trace amounts of protons, neutrons and electrons. At this energy, nuclear interactions are rapid and keep small equilibrium abundances of the light elements. As the temperature continues to fall, the abundances of the light elements grow; these are deuterium (D), tritium (T), helium (3He & 4He), lithium (7Li) and beryllium (7Be). Being the most strongly bound nuclei, 4He's abundance grows most rapidly, but we run into a problem. The cosmic nuclear reactor stalls. The ¯rst step in forming 4He is the production of D from the collision of a neutron and proton. Due to the fact that photons out-number baryons by 1 billion, as soon as D forms, it is destroyed. Because of this, the burning into heavier elements is suppressed. In fact, we have to wait for the universe to cool su±ciently, so that the fraction of photons having enough energy to destroy D is smaller than baryon-to-photon ratio, a temperature of about 0.07 MeV. This is known as the deuterium bottleneck.

Once we produce D, we rapidly lock it into 4He. The Coulomb barrier as well as the lack of stable elements with atomic mass numbers 5 and 8, inhibits the production of nuclei with mass numbers larger than 7. Once the universe cools enough, the Coulomb barrier between nuclei becomes su±ciently large that nucleosynthesis comes to a halt. So ends the epoch of primordial nucleosynthesis. The predictions of this theory are shown in figure 1.1, plotted against BBN's one free parameter, .

Figure 1.1: The light element abundance predictions from BBN theory plotted against the baryon-to-photon ratio, . From top to bottom are the mass fraction of 4He and the relative mole fractions D/H, 3He/H and 7Li/H. The shaded bands enclose the 1 region.