A Finslerian Cosmological Metric and its Riemannian Kaluza-Klein Extension

TL;DR

This paper explores a Finslerian cosmological metric and its Riemannian Kaluza-Klein extension, revealing cosmological solutions with domain wall and string dominated internal spaces, bridging Finsler and Riemannian geometries in cosmology.

Contribution

It introduces a novel Finslerian metric invariant under rotations and translations, and extends it to a higher-dimensional Riemannian space with equivalent geodesics.

Findings

Cosmological solutions exhibit equations of state for domain walls and strings.

The Finslerian and Riemannian geodesics are equivalent under specific coordinate conditions.

The model provides a new geometric framework for cosmological matter content.

Abstract

In this study a rotationally and translationally invariant metric in Finsler space is investigated. We choose to rewrite the metric in Riemanian space by increasing the dimension of space-time and introducing additional coordinates such that for specific values of these coordinates, the geodesics of the four dimensional Finslerian space-time and six dimensional Riemanian space-time are identical. Cosmological solutions described by this metric give rise to an equation of state corresponding to a space dominated by domain walls and an internal space dominated by strings.