Astroparticle Physics

21310 Big Bang Nucleosynthesis“In fact, it seems that present day science,with one sweeping step back across millionsof centuries, has succeeded in bearing witnessto that primordial ‘Fiat lux’ [let therebe light] uttered at the moment when, alongwith matter, there burst forth from nothinga sea of light and radiation, while the particlesof the chemical elements split andformed into millions of galaxies. Hence, creationtook place in time, therefore, there is aCreator, therefore, God exists!”Pope Pius XIIAt times from around 10 −2 seconds through the first severalminutes after the Big Bang, the temperature passed throughthe range from around 10 to below 10 −1 MeV. During thisperiod protons and neutrons combined to produce a significantamount of 4 He – one quarter of the universe’s nucleiby mass – plus smaller amounts of deuterium (D, i.e., 2 H),tritium ( 3 H), 3 He, 6 Li, 7 Li, and 7 Be. Further synthesis of nucleiin stars accounts for all of the heavier elements plus onlya relatively small additional amount of helium. The predictionsof Big Bang Nucleosynthesis (BBN) are found to agreeremarkably well with observations, and provide one of themost important pillars of the Big Bang model.The two main ingredients of BBN are the equations ofcosmology and thermal physics that have already been described,plus the rates of nuclear reactions. Although the nuclearcross sections are difficult to calculate theoretically,they have for the most part been well measured in laboratoryexperiments. Of crucial importance is the rate of thereaction ν e n ↔ e − p, which allows transformation betweenneutrons and protons. The proton is lighter than the neutronby m = m n − m p ≈ 1.3 MeV, and as long as this reactionproceeds sufficiently quickly, one finds that the neutron-to-protonratio is suppressed by the Boltzmann factore −m/T . 1 At a temperature around 0.7 MeV the reaction isno longer fast enough to keep up and the neutron-to-protonratio ‘freezes out’ at a value of around 1/6. To first approximationone can estimate the helium abundance simply byassuming that all of the available neutrons end up in 4 He.1 In the following the natural constants c, ¯h,andk are set to unity.primordial elementsBig Bang Nucleosynthesistransformation betweenneutrons and protonsfreeze-out temperature