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

## TL;DR

This paper develops a generalized framework extending General Relativity on the tangent Lorentz bundle, incorporating local anisotropy and weak perturbations, leading to new insights into cosmological acceleration and bounce phenomena.

## Contribution

It introduces a geometrical extension of GR with local anisotropy on the tangent bundle, deriving new field equations, generalized wave equations, and cosmological models.

## Key findings

- Accelerated universe expansion attributed to geometry.
- Modeling of a cosmological bounce with anisotropic scalar field.
- Generalization of Klein-Gordon and dispersion relations.

## 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.