Big Bang Nucleosynthesis

Abstract

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 [2][3][4] for reviews). 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, and on new physics beyond the Standard Model [5-8]. TheoryThe synthesis of the light elements is sensitive to physical conditions in the early radiation-dominated era at a temperature 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 per nucleon, 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 (see 'Big Bang Cosmology' review). 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 [9]. After freeze-out, the neutrons were free to β-decay, so the neutron fraction dropped to n/p ≃ 1/7 by the time nuclear reactions began. A simplified analytic model of freeze-out yields the n/p ratio to an accuracy of ∼ 1% [10,11].The rates of these reactions depend on the density of baryons (strictly speaking, nucleons), which is usually expressed normalized to the relic blackbody photon density as η ≡ n b /n γ . As we shall see, all the light-element abundances can be explained with η 10 ≡ η × 10 10 in the range 5.7-6.7 (95% CL). With n γ fixed by the present CMB temperature 2.7255 K (see 'Cosmic Microwave Background' review), this can be stated as the allowed range for the baryon mass density today, ρ b = (3.9-4.6) × 10 −31 g cm −3 , or as the baryonic fraction of the critical density, Ω b = ρ b /ρ crit ≃ η 10 h −2 /274 = (0.021-0.025)h −2 , where h ≡ H 0 /100 km s −1 Mpc −1 is the present Hubble parameter (see Cosmological Parameters review).The nucleosynthesis chain begins with the formation of deuterium in the process p(n, γ)D. However, photo-dissociation by the high number density of photons delays