Stochastic Finsler D-particle Space-Time Foam Enhances Dark Matter Relics

Within the context of space-time (D-particle) foam in string/brane-theory it is demonstrated that it is possible to generate non-extensive statistics. The D-particle foam model involves point-like brane defects (D-particles), which provide the topologically non-trivial foamy structures of space-time. The D-particles can capture and emit stringy matter and this leads to a recoil of D-particles. It is indicated how one effect of such a recoil of D-particles is a back reaction on the space-time metric of Finsler type which is stochastic. We show that such a type of stochastic space-time foam can lead to cosmological effects similar to those induced by modifications of particle distributions within the framework of Tsallis entropies. The restrictions placed on the free parameters of the Finsler type metric are obtained from solving the Boltzmann equation in this background for relic abundances of a Lightest Supersymmetric Particle (LSP) dark matter candidate. It is demonstrated that the D-foam acts as a source for particle production in the Boltzmann equation, thereby leading to enhanced thermal LSP relic abundances relative to those in the Standard Lambda CDM Cosmology. For D-particle masses of order TeV, such effects may be relevant for dark matter searches at colliders. The latter constraints complement those coming from high energy gamma-ray astronomy on the induced vacuum refractive index that D-foam models entail.