  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.
