Non-extensive statistics and its effects on cosmology

TL;DR

This paper explores how non-extensive Tsallis statistics influence cosmological models, revealing effects like fractal scaling in radiation eras and significant impacts on dark matter relic abundances, with implications for phenomenology and quantum gravity models.

Contribution

It introduces the application of Tsallis statistics to supercritical string cosmology, demonstrating novel effects on cosmological evolution and dark matter relics, and links these to D-particles foam models.

Findings

Fractal scaling naturally emerges in radiation-dominated eras.

Relic abundances of neutralinos are significantly affected.

D-particles foam can produce similar statistical effects.

Abstract

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.