De Sitter vacua in ghost-free massive gravity theory

TL;DR

This paper introduces a method to find all de Sitter solutions in ghost-free massive gravity using the Gordon ansatz, revealing infinitely many vacua with potential stability and implications for cosmology.

Contribution

The paper provides a systematic procedure to obtain all de Sitter solutions in ghost-free massive gravity, highlighting the existence of infinitely many vacua with different stability properties.

Findings

Infinite de Sitter vacua with varying properties

The simplest solution is unstable, others may be stable

Solutions can be non-manifestly homogeneous and isotropic

Abstract

We present a simple procedure to obtain all de Sitter solutions in the ghost-free massive gravity theory by using the Gordon ansatz. For these solutions the physical metric can be conveniently viewed as describing a hyperboloid in 5D Minkowski space, while the flat reference metric depends on the Stuckelberg field $T(t,r)$ that satisfies the equation $(\partial_t{T})^2-(\partial_r T)^2=1$. This equation has infinitely many solutions, hence there are infinitely many de Sitter vacua with different physical properties. Only the simplest solution with $T=t$ has been previously studied since it is manifestly homogeneous and isotropic, but it is unstable. However, other solutions could be stable. We require the timelike isometry to be common for both metrics, and this gives physically distinguished solutions since only for them the canonical energy is time-independent. We conjecture that these solutions minimize the energy and are therefore stable. We also show that in some cases solutions can be homogeneous and isotropic in a non-manifest way such that their symmetries are not obvious. All of this suggests that the theory may admit viable cosmologies.