Non-extensive statistics and its effects on cosmology

Non-extensive statistics, namely Tsallis statistics, is applied on a case of a supercritical string cosmology and interesting cosmological modifications are obtained. The two main results we focus on in this work are: fractal scaling for relativisitic matter which occurs naturally in a radiation dominated era and effects (maybe considerable) on the relic abundances of supersymmetric dark matter candidates (neutralinos) which are obtained by solving the modified Boltzmann equation. In fact these last effects can be linked to a very rich phenomenology yielding important restrictions.In the end of the paper we also give the general framework of the D-particles foam model, which as proved can give rise to statistical effects similar to Tsallis effects, by basically assuming a stochastic gravitational background.