Friedmann Robertson-Walker model in generalised metric space-time with weak anisotropy

A generalized model of space-time is given, taking into consideration the anisotropic structure of fields which are depended on the position and the direction (velocity).In this framework a generalized FRW-metric the Raychaudhouri and Friedmann equations are studied.A long range vector field of cosmological origin is considered in relation to the physical geometry of space-time in which Cartan connection has a fundamental role.The generalised Friedmann equations are produced including anisotropic terms.The variation of anisotropy $z_t$ is expressed in terms of the Cartan torsion tensor of the Finslerian space-time.A possible estimation of the anisotropic parameter $z_t$ can be achieved with the aid of the de-Sitter model of the empty flat universe with weak anisotropy. Finally a physical generalisation for the model of inflation is also studied.Comment: 21 pages- to appear in GR

Super-Luminal Effects for Finsler Branes as a Way to Preserve the Paradigm of Relativity Theories

Using Finsler brane solutions [see details and methods in: S. Vacaru, Class. Quant. Grav. 28 (2011) 215001], we show that neutrinos may surpass the speed of light in vacuum which can be explained by trapping effects from gravity theories on eight dimensional (co) tangent bundles on Lorentzian manifolds to spacetimes in general and special relativity. In nonholonomic variables, the bulk gravity is described by Finsler modifications depending on velocity/ momentum coordinates. Possible super-luminal phenomena are determined by the width of locally anisotropic brane (spacetime) and induced by generating functions and integration functions and constants in coefficients of metrics and nonlinear connections. We conclude that Finsler brane gravity trapping mechanism may explain neutrino super-luminal effects and almost preserve the paradigm of Einstein relativity as the standard one for particle physics and gravity.Comment: latex2e, 15 pages, v3, accepted to: Foundations of Physics 43 (2013

Generalized-Finslerian equation of geodesic deviations

We indicate that the main term in the geodesic deviation equation is given by the generalized torsion tensor. In the static spherically-symmetric case, the explicit representation for the main term is found in the first-order low-velocity approximation. © 1993

Congruences of fluids in a Finslerian anisotropic space-time

We derive the generalized Raychauduri equation concepts of expansion, shear and vorticity. We give the Ricci tensor of a constant-curvature Randers-Finsler space metric whose first term is the Robertson-Walker metric. © 2005 Springer Science + Business Media, Inc

Tidal forces in vertical spaces of Finslerian space-time

The classical equation of geodesic deviation is extended in the case of vertical geodesics associated with a Finslerian space-time. It is shown that the deviations can appear only if the vertical component of the energy-momentum tensor differs from zero. © 1992

Raychaudhuri equation in the Finsler-Randers space-time and generalized scalar-tensor theories

In this work, we obtain the Raychaudhuri equations for various types of Finsler spaces as the Finsler-Randers (FR) space-time and in a generalized geometrical structure of the space-time manifold which contains two fibers that represent two scalar fields φ(1),φ(2). We also derive the Klein-Gordon equation for this model. In addition, the energy conditions are studied in a FR cosmology and are correlated with FRW model. Finally, we apply the Raychaudhuri equation for the model M ×φ(1)×φ(2), where M is a FRW-space-time. © 2018 World Scientific Publishing Company

Finslerian deviations of Geodesics over tangent bundle

The geodesic deviation equation is derived in the framework of the fibered Finslerian gauge approach, under the general conditions when all the Finslerian curvature and torsion tensors are taken into account. Just as the Riemannian curvature tensor enters the equation of deviation of Riemannian geodesics, the Yang-Mills-type gauge tensor proves to govern the behaviour of the vertical part of the Finslerian deviations, thereby exhibiting its observable nature. © 1992

Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle

We study field equations for a weak anisotropic model on the tangent Lorentz bundle TM of a spacetime manifold. A geometrical extension of general relativity (GR) is considered by introducing the concept of local anisotropy, i.e. a direct dependence of geometrical quantities on observer 4-velocity. In this approach, we consider a metric on TM as the sum of an h-Riemannian metric structure and a weak anisotropic perturbation, field equations with extra terms are obtained for this model. As well, extended Raychaudhuri equations are studied in the framework of Finsler-like extensions. Canonical momentum and mass-shell equation are also generalized in relation to their GR counterparts. Quantization of the mass-shell equation leads to a generalization of the Klein-Gordon equation and dispersion relation for a scalar field. In this model the accelerated expansion of the universe can be attributed to the geometry itself. A cosmological bounce is modeled with the introduction of an anisotropic scalar field. Also, the electromagnetic field equations are directly incorporated in this framework. © 2018 IOP Publishing Ltd

Nonlocalized field theory over spinor bundles: Poincaré gravity and Yang-Mills fields

In this paper we study the differential structure of a spinor bundle in spaces where the metric tensor gμν(x, ξ, \ ̄gx) of the base manifold depends on the position x as well as on the spinor variables ξ and \ ̄gx. Notions such as: gauge covariant derivatives of tensors, connections, curvatures, torsions and Bianchi identities are presented in the context of a gauge approach, different than the one proposed in [11, 13], due to the introduction of a Poincaré group and the use of d-connections [6, 8] in the spinor bundle S(2) M. The introduction of basic 1-form fields ρ{variant}μ and spinors ζa, \ ̄gza with values in the Lie algebra of the Poincaré group is also essential in our study. The gauge field equations are derived by the authors [12]. Finally, we give the Yang-Mills and the Yang-Mills-Higgs equations in a form sufficiently generalized for our approach. © 1995