Astroparticle Physics

214 10 Big Bang Nucleosynthesisbaryon densityThe one free parameter of BBN is the baryon density Ω bor, equivalently, the baryon-to-photon ratio η. By comparingthe observed abundances of the light elements with thosepredicted by BBN, the value of η can be estimated. The resultwill turn out to be of fundamental importance for thedark-matter problem, which will be dealt with in Chap. 13.10.1 Some Ingredients for BBN“The point of view of a sinner is that thechurch promises him hell in the future,but cosmology proves that the glowinghell was in the past.”Ya.B.Zel’dovichexpansion rateingredients for BBNdisappearance of antimatterneutrino familiesTo model the synthesis of light nuclei one needs the equationsof cosmology and thermal physics relevant for temperaturesin the MeV range. At this point the total energydensity of the universe is still dominated by radiation (i.e.,relativistic particles), so the pressure and energy density arerelated by P = ϱ/3. In Chap. 9 it was shown that this ledto relations for the expansion rate and time as a function oftemperature,H = 1.66 √ T 2g ∗ , (10.1)m Plt = 0.301 m Pl√g∗ T 2 . (10.2)To use these equations one needs to know the effectivenumber of degrees of freedom g ∗ . Recall that quarks andgluons have already become bound into protons and neutronsat around T = 200 MeV, and since the nucleon mass isaround m N ≈ 0.94 GeV, these are no longer relativistic. Nucleonsand antinucleons can remain in thermal equilibriumdown to temperatures of around 50 MeV, and during this periodtheir number densities are exponentially suppressed bythe factor e −mN/T . At temperatures below several tens ofMeV the antimatter has essentially disappeared and the resultingnucleon density therefore does not make a significantcontribution to the energy density.At temperatures in the MeV range, the relativistic particlesare photons, e − , ν e , ν µ , ν τ , and their antiparticles. Thephotons contribute g γ = 2ande + and e − together giveg e = 4. In general, if there are N ν families of neutrinos,