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

TL;DR

This paper develops a generalized Friedmann-Robertson-Walker cosmological model incorporating weak anisotropy and Finslerian geometry, deriving new equations and exploring implications for inflation and anisotropic parameters.

Contribution

It introduces a generalized FRW model with anisotropic terms using Cartan connection in Finslerian space-time, extending classical cosmology frameworks.

Findings

Derived generalized Friedmann equations with anisotropic terms

Expressed anisotropy variation in terms of Cartan torsion tensor

Estimated anisotropic parameter using de-Sitter model

Abstract

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.