# Cosmological solutions and finite time singularities in Finslerian geometry

## TL;DR

This paper explores cosmological models within Finslerian geometry, deriving gravitational equations, analyzing various universe evolutions including singularities and bounces, and establishing thermodynamics laws in this generalized geometric framework.

## Contribution

It introduces a general Finslerian cosmological model with a novel equation of state, analyzing diverse universe scenarios and their singularity behaviors.

## Key findings

- Multiple cosmological evolutions depending on the parameter γ
- Existence of finite time singularities and nonsingular accelerating universes
- Thermodynamics laws are applicable in Finslerian spacetime

## Abstract

We consider a very general scenario of our universe where its geometry is characterized by the Finslerian structure on the underlying spacetime manifold, a generalization of the Riemannian geometry. Now considering a general energy-momentum tensor for matter sector, we derive the gravitational field equations in such spacetime. Further, to depict the cosmological dynamics in such spacetime proposing an interesting equation of state identified by a sole parameter $\gamma$ which for isotropic limit is simply the barotropic equation of state $p= (\gamma- 1) \rho$ ($\gamma \in \mathbb{R}$ being the barotropic index), we solve the background dynamics. The dynamics offers several possibilities depending on this sole parameter as follows $-$ (i) only an exponential expansion, or (ii) a finite time past singualrity (big bang) with late accelerating phase, or (iii) a nonsingular universe exhibiting an accelerating scenario at late time which finally predicts a big rip type singularity. We also discuss several energy conditions and the possibility of cosmic bounce. Finally, we establish the first law of thermodynamics in such spacetime.