Abstract
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 ΛCDM 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.
Highlights
There has been recent interest in physics beyond the Standard Model which can incorporate Lorentz symmetry violations [1] in a Finsler geometry setting [2,3,4]
Just as candidates for Dark Matter have to be sought from Physics beyond the Standard Model, we need to have a framework which goes beyond local effective Lagrangians, to incorporate the Finsler dynamical background
The foam acts as a source of particle production [7], and affects particle statistics in a way reminiscent of non-extensive statistics of Tsallis type
Summary
There has been recent interest in physics beyond the Standard Model which can incorporate Lorentz symmetry violations [1] in a Finsler geometry setting [2,3,4]. The interaction of material open strings (such as photons) with the D-particles leads to an induced distortion of space-time described by a metric, which depends on both the coordinate and momentum transfer of the photon during its scattering with the defect and so has similarities to a Finsler metric [2] This is a topologically non-trivial process, involving the creation of a non-local intermediate string state, oscillating from zero length to a maximum one, according to a time-space stringy uncertainty [10, 22]. Technical aspects of the work are presented in two appendices
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