Implications of a Stochastic Microscopic Finsler Cosmology
  Within the context of supersymmetric space-time (D-particle) foam in
string/brane-theory, we discuss a Finsler-induced Cosmology and its
implications for (thermal) Dark Matter abundances. This constitutes a truly
microscopic model of dynamical space-time, where Finsler geometries arise
naturally. 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 acceptable cosmologies at late epochs of the Universe, due to the
non-trivial properties of the supersymmetric (BPS like) D-particle defects,
which are such so as not to affect significantly the Hubble expansion. 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 LambdaCDM 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. We also comment briefly on the production mechanisms of such
TeV-mass stringy defects at colliders, which, in view of the current LHC
experimental searches, will impose further constraints on their couplings.
