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

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.

31 pages

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Cited by in corpus (6)

• Dynamics in Varying vacuum Finsler-Randers Cosmology
• Bounce cosmology in generalized modified gravities
• Searches for beyond-Riemann gravity
• On the analyticity of static solutions of a field equation in Finsler gravity
• Anisotropic Conformal Dark Gravity on the Lorentz Tangent Bundle Spacetime
• Raychaudhuri equations, Tidal forces and Weak field Limit in Schwarzshild-Finsler-Randers spacetime