Implications of a stochastic microscopic Finsler cosmology

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.

Cosmic magnetization in curved and Lorentz violating space–times

“…All this phenomenology and cosmological constraints combined with particular QG theories where the effective geometry is Finslerian can give a better insight about LV and the colorful morphology of the physical manifold. This detailed and complicated analysis is an intriguing open challenge (for some recent studies see [91][92][93][94][95][96][153][154][155][156][157][158][159][160]). Since our amplification mechanism strongly depends on the intensity of Cartan tensor and its evolution in time, constraining the 'Finslerity' of space-time may lead to a better understanding of why our universe is magnetized.…”

“…They may be physically interpreted as an arbitrary direction at each tangent space induced by the breaking of Lorentz invariance (see for example [110,112]). In fact, Finsler geometry is encountered in Lorentz violating branches of quantum gravity [86][87][88][89][90][91][92][93][94][95][96][97][98][99][100][101] and also effectively describes motion in anisotropic media [113,114]. Apart from the metric tensor (1) there is another important geometric entity, the Cartan tensor…”

“…Motivated by the previous analysis we use Finsler geometry as our theoretical background to study LV (see for example ). In addition, Finsler geometry is encountered in many branches of QG like SME [59][60][61], Horava-Lifshitz gravity [86,87], holographic fluids [88][89][90], D-particle space-time foam [91][92][93][94][95][96], very special relativity [97,98], Galilean transformations in curved space-time [99], bi-metric theories of gravity [100] and plays a keynote role in the analog gravity program [101]. In Finsler geometry the local structure of GR is extended by adopting a non-quadratic line element [102][103][104][105].…”

Nonholonomic Ricci Flows of Riemannian Metrics and Lagrange-Finsler Geometry

“…On manifold V, the equations (24) and (25) τ The evolution of such N-adapted frames is not defined by the equations (26) but satisfies the Proposition 4.1: For a prescribed n+m splitting, the solutions of the system (24) and (25) (27) and the set of dual frame (coframe) structures ( ) = ( , ( )), (26), we can extract a set of preferred frame structures with associated N-connections, with respect to which we can perform the geometric constructions in N-adapted form.…”

“…Recently, a number of applications in physics of the Ricci flow theory were proposed, by Vacaru [12][13][14][15][16].Some geometrical approaches in modern gravity and string theory are connected to the method of moving frames and distributions of geometric objects on (semi) Riemannian manifolds and their generalizations to spaces provided with nontrivial torsion, nonmetricity and/or nonlinear connection structures [17,18]. The geometry of nonholonomic manifolds and non-Riemannian spaces is largely applied in modern mechanics, gravity, cosmology and classical/quantum field theory expained by Stavrinos [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Such spaces are characterized by three fundamental geometric objects: nonlinear connection (N-connection), linear connection and metric.…”