Cosmology Based on Finsler and Finsler-like Metric Structure of Gravitational Field

TL;DR

This paper reviews how Finsler and Finsler-like geometries extend gravitational and cosmological models, introducing anisotropic effects and new degrees of freedom, and explores their implications for universe evolution and phenomena like the gravitational Magnus effect.

Contribution

It presents a comprehensive review of Finsler-based gravitational and cosmological models, highlighting their ability to incorporate anisotropic phenomena and extend general relativity.

Findings

Finsler geometries introduce anisotropic terms in cosmological equations.

Finsler-Randers and Schwarzschild Finsler-Randers models describe universe evolution.

The approach recovers GR when anisotropic terms are omitted.

Abstract

In this article, we review some aspects of gravitational field and cosmology based on Finsler and Finsler-like generalized metric structures. The geometrical framework of these spaces allows further investigation of locally-anisotropic phenomena related to the gravitational field and cosmological considerations, e.g the extracted geodesics, deflection of light, Finsler-Einstein gravitational field equations , the Friedmann equations and the Raychaudhuri equations include extra anisotropic terms that in the Riemannian framework of General Relativity (GR) are not interpreted. This approach gives us the opportunity to extend the research with more degrees of freedom on the tangent bundle of a spacetime manifold. In the above mentioned generalizations omitting the extra anisotropic terms we recover the framework of GR. In addition, we study the gravitational Magnus effect in a generalized metric framework. Based on this approach, we describe further properties of Finsler-Randers (FR) and Schwarzschild Finsler Randers (SFR) cosmological models which are useful for the description and evolution of the universe.