Big Bang Nuclesynthesis

Abstract

The big bang nucleosynthesis (BBN) is the process of production of light elements in the early Universe, a few minutes after the big bang. The theoretical predictions of the abundances of deuterium, helium-3, helium-4, and lithium-7 are determined by the Friedmann equations, the matter content of the Standard Model of particle physics, and a large number of particle properties and nuclear reaction rates that can be measured in laboratory. With all this knowledge, the outcome of the production is determined by a single free parameter, the ratio of the baryon to photon number densities, $\eta$. From the comparison of theoretical predictions and observational data of the primordial abundances, it is possible to infer the value of $\eta$. Independent measurements from different light elements are all consistent with $\eta$ in the range $10^{-10} - 10^{-9}$, and this is seen as a great success of the theoretical framework and one of the milestones of the Standard Model of cosmology. Today $\eta$ can be measured from the CMB with high precision, and the result is in a very good agreement with the determination of $\eta$ from the BBN. Nevertheless, this value is in conflict with the observed abundance of non-relativistic matter in the contemporary Universe. This suggests that most of the matter in galaxies is not made of ordinary matter like protons and neutrons, but more likely of particles not belonging to the Standard Model of particle physics.

Problems

8.1

What is the effect on the abundance of primordial helium-4 in the following cases?

• (a) The lifetime of neutrons is longer/shorter.

• (b) The tauon neutrino has a mass $m_{\nu _\tau } \approx 10$ MeV.

• (c) The deuterium binding energy is higher/lower.