Question

Consider a ‘gas’ of charged particles in the early Universe with g ≃ 100 and charge e. By comparing the
thermal and Coulomb interaction energies, argue that we can treat the system as non-interacting. (Ignore
numerical factors of order unity – we are looking for an order of magnitude style answer here.)

g is the # of spin degrees of freedom

Answer 1

we will compare the Early universe thermal situation by basically dealing with the rate of interaction vs rate of expansion. If see the calculation the ratio of thermal Energy to coloumbic is .

which is very very large amount. Thus, coloumbic interactions were negligible in compared to thermal energy due to the pressure of state densities of all particles in a gas. Thus, they were very weakly interacting and thus non-interacting bodies. Thus, we can assume that the system was statistically independent so that the statistical weight of the universe (system) is a product and entropy is a sum.