All nuclei are built up of protons and neutrons. Before we explore the nuclear reactions that synthesize deuterium, helium, lithium, etc., we therefore examine the abundances of their building blocks. Protons and neutrons have a very comparable rest mass of ~940 MeV, which implies that they become non-relativistic at very early times (t≃10-6 s, T ≃ 1013 K). Down to a temperature of ~0.8 MeV they maintain thermal
In thermal equilibrium, their number densities follow from Eq. (2):
where we have used that both protons and neutrons have two helicity states 
Writing the mass difference as 
, and using 
, we obtain the ratio between the number densities of protons and neutrons in thermal equilibrium:
where 
. When T ≫ 
the reactions (1) go equally fast in both directions and there are as many protons as neutrons. When the temperature decreases towards ~1 MeV, however, the number density of neutrons starts to drop with respect to that of protons, because neutron is slightly more massive. If thermal equilibrium were to be maintained, the ratio would continue to decrease to very small values. However, at about the same temperature of 
neutrinos start to decouple. Therefore, the rate of the weak reactions (1) is no longer fast enough to establish thermal equilibrium against the expansion rate of the Universe, and the ratio
will eventually ‘freeze out’ at a value of 
. However, neutrons are unstable to beta decay,
so that even after freeze-out the neutron-to-proton ratio continues to decrease. If we define the neutron abundance as
then it evolves due to the neutron decay as
where 
is the mean lifetime of neutrons. The main reason that the present-day Universe contains a large abundance of neutrons is that, shortly before the Universe reaches an age 
, most neutrons have already ended up in helium nuclei (which stabilizes them against beta decay due to Pauli’s exclusion principle) through the process of nucleosynthesis to be described below.
