bbn - 20. Big-Bang nucleosynthesis 1 20. BIG-BANG...

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20. Big-Bang nucleosynthesis 1 20. BIG-BANG NUCLEOSYNTHESIS Revised October 2005 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 [1–4]. 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 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]. 20.1. 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 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 , 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 a±ords 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 simplified analytic model of freeze-out yields the n/p ratio to an accuracy of 1% [7,8]. 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 4 . 7–6 . 5 (95% CL). With n γ fixed 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 . 2–4 . 5) × 10 - 31 g cm - 3 , or as the baryonic fraction of the critical density, Ω B = ρ B crit ± η 10 h - 2 / 274 = (0 . 017–0 . 024) h - 2 , where h H 0 /
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This note was uploaded on 08/01/2008 for the course ASTRO 228 taught by Professor Chungpeima during the Fall '06 term at University of California, Berkeley.

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bbn - 20. Big-Bang nucleosynthesis 1 20. BIG-BANG...

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