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arXiv · 1903.12521

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

A. Triantafyllopoulos·P. C. Stavrinos
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Abstract

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.

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A. Triantafyllopoulos, P. C. Stavrinos. 2019-03-29. Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle. https://doi.org/10.1088/1361-6382%2Faab27f

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