ar X iv : a st ro - p h / 04 06 66 3 v 1 2 9 Ju n 20 04 1 . Big - bang nucleosynthesis 1 1 . BIG - BANG NUCLEOSYNTHESIS

Big-bang nucleosynthesis (BBN) offers the deepest reliable probe of the early universe, being based on well-understood Standard Model physics [1]. Predictions of the abundances of the light elements, D, 3 He, 4 He, and 7 Li, synthesized at the end of the " first three minutes " are in good overall agreement with the primordial abundances inferred from observational data, thus validating the standard hot big-bang cosmology (see [5] for a recent review). This is particularly impressive given that these abundances span nine orders of magnitude — from 4 He/H ∼ 0.08 down to 7 Li/H ∼ 10 −10 (ratios by number). Thus BBN provides powerful constraints on possible deviations from the standard cosmology [2], and on new physics beyond the Standard Model [3]. 1.1. Big-bang nucleosynthesis theory The synthesis of the light elements is sensitive to physical conditions in the early radiation-dominated era at temperatures T < ∼ 1 MeV, corresponding to an age t > ∼ 1 s. At higher temperatures, weak interactions were in thermal equilibrium, thus fixing the ratio of the neutron and proton number densities to be n/p = e −Q/T , where Q = 1.293 MeV is the neutron-proton mass difference. As the temperature dropped, the neutron-proton inter-conversion rate, Γ n↔p ∼ G 2 F T 5 , fell faster than the Hubble expansion rate, H ∼ √ g * G N T 2 , where g * counts the number of relativistic particle species determining the energy density in radiation. This resulted in departure from chemical equilibrium (" freeze-out ") at T fr ∼ (g * G N /G 4 F) 1/6 ≃ 1 MeV. The neutron fraction at this time, n/p = e −Q/T fr ≃ 1/6, is thus sensitive to every known physical interaction, since Q is determined by both strong and electromagnetic interactions while T fr depends on the weak as well as gravitational interactions. Moreover the sensitivity to the Hubble expansion rate affords a probe of e.g. the number of relativistic neutrino species [6]. After freeze-out the neutrons were free to β-decay so the neutron fraction dropped to ≃ 1/7 by the time nuclear reactions began. A useful semi-analytic description of freeze-out has been given [7]. The rates of these reactions depend on the density of baryons (strictly speaking, nucleons), which is usually expressed normalized to the blackbody photon density as η ≡ n B /n γ. As we …