# Anisotropic deformations of spatially open cosmology in massive gravity theory

## TL;DR

This paper investigates how anisotropic deformations in open cosmology within massive gravity evolve, showing relaxation to isotropic de Sitter states or singular outcomes depending on initial perturbation strength.

## Contribution

It introduces new insights into the evolution of anisotropic perturbations in massive gravity and presents a family of novel homogeneous and isotropic cosmologies.

## Key findings

- Weak perturbations relax to de Sitter state with anisotropies damped
- Strong perturbations lead to singular anisotropic states or decay to flat spacetime
- New family of homogeneous and isotropic cosmologies discovered

## Abstract

We study anisotropic deformations of the spatially open homogeneous and isotropic cosmology in the ghost free massive gravity theory with flat reference metric. We find that if the initial perturbations are not too strong then the physical metric relaxes back to the isotropic de Sitter state. However, the dumping of the anisotropies is achieved at the expense of exciting the Stueckelberg fields in such a way that the reference metric changes and does not share anymore with the physical metric the same rotational and translational symmetries. As a result, the universe evolves towards a fixed point which does not coincide with the original solution, but for which the physical metric is still de Sitter. If the initial perturbation is strong, then its evolution generically leads to a singular anisotropic state or, for some parameter values, to a decay into flat spacetime. We also present an infinite dimensional family of new homogeneous and isotropic cosmologies in the theory.