Finsler fluid dynamics in $\mathrm{SO}(4)$ symmetric cosmology

TL;DR

This paper develops a general framework for Finsler spacetime geometry with $ ext{SO}(4)$ symmetry and derives fluid dynamics equations consistent with this symmetry, advancing the understanding of anisotropic cosmological models.

Contribution

It introduces a comprehensive Finsler geometric model for $ ext{SO}(4)$ symmetric cosmology and formulates the corresponding kinetic fluid equations.

Findings

Derived equations of motion for Finsler fluids with $ ext{SO}(4)$ symmetry.

Proposed a coordinate system simplifying symmetry generators.

Established a foundation for studying anisotropic cosmological fluids.

Abstract

We discuss the most general Finsler spacetime geometry obeying the cosmological symmetry group $\mathrm{SO}(4)$. On this background geometry we derive the equations of motion for the most general kinetic fluid obeying the same cosmological symmetry. For this purpose we propose a set of coordinates on the tangent bundle of the spacetime manifold which greatly simplifies the cosmological symmetry generators.