Cosmology in a non-standard statistical background

We study the primordial neutron to baryon ratio in a cosmological expanding background within the context of non-extensive statistics, in a fully analytical approach. First order corrections to the weak interaction rates and energy densities in the early universe are obtained and their consequences on the Helium synthesis are analyzed. We find that, if the nucleosynthesis scenario should be in agreement with observation, this entails a very restrictive bound upon q, the non-extensive parameter. We also study some cosmologically interesting situations such as the moment of pair annihilation, conserved comoving quantities and derive for the nonextensive statistics, temperature relationships, before and after the removal of pairs.