rpp2010-rev-bbang-nucleosynthesis - 20. Big-Bang...

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20. Big-Bang nucleosynthesis 1 20. BIG-BANG NUCLEOSYNTHESIS Revised August 2009 by B.D. Fields (Univ. of Illinois) and S. Sarkar (Univ. of Oxford). Big-Bang nucleosynthesis (BBN) o±ers the deepest reliable probe of the early Universe, being based on well-understood Standard Model physics [1–5]. Predictions of the abundances of the light elements, D, 3 He, 4 He, and 7 Li, synthesized at the end of the ‘²rst three minutes’, are in good overall agreement with the primordial abundances inferred from observational data, thus validating the standard hot Big-Bang cosmology (see [6] for a 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 [3,4]. 20.1. Theory The 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 1s. At higher temperatures, weak interactions were in thermal equilibrium, thus ²xing 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 di±erence. 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 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 ± 1M eV . The neutron fraction at this time, n/p 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 a±ords a probe of e.g., the number of relativistic neutrino species [7]. 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 simpli²ed analytic model of freeze-out yields the n/p ratio to an accuracy of 1% [8,9]. 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 . 1–6 . 5 (95% CL). With n γ ²xed by the present CMB temperature 2.725 K (see ‘Cosmic Microwave Background’ review), this can be stated as the allowed range for the baryon mass density today, ρ b =(3 . 5–4 . 5) × 10 31 gcm 3 ,o ra sth e baryonic fraction of the critical density, Ω b = ρ b crit ± η 10 h 2 / 274 = (0 . 019–0 . 024) h 2 , where h H 0 / 100 km s 1 Mpc 1 =0 . 72 ² 0 . 08 is the present Hubble parameter (see Cosmological Parameters review).
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rpp2010-rev-bbang-nucleosynthesis - 20. Big-Bang...

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