On Cosmic No-hair in Bimetric Gravity and the Higuchi Bound

TL;DR

This paper investigates the cosmic no-hair conjecture within bimetric gravity, demonstrating stable de Sitter solutions, the conditions for cosmic no-hair validity, and the critical role of the Higuchi bound in stability and solution bifurcation.

Contribution

It provides the first analysis of cosmic no-hair in bimetric gravity, revealing the connection between solution stability, the Higuchi bound, and the violation or preservation of cosmic no-hair.

Findings

Stable de Sitter solutions exist with a cosmological constant in the physical sector.

One branch of solutions is always stable under anisotropic perturbations.

The bifurcation point of solution branches coincides with the Higuchi bound.

Abstract

We study the cosmic no-hair in the presence of spin-2 matter, i.e. in bimetric gravity. We obtain stable de Sitter solutions with the cosmological constant in the physical sector and find an evidence that the cosmic no-hair is correct. In the presence of the other cosmological constant, there are two branches of de Sitter solutions. Under anisotropic perturbations, one of them is always stable and there is no violation of the cosmic no-hair at the linear level. The stability of the other branch depends on parameters and the cosmic no-hair can be violated in general. Remarkably, the bifurcation point of two branches exactly coincides with the Higuchi bound. It turns out that there exists a de Sitter solution for which the cosmic no-hair holds at the linear level and the effective mass for the anisotropic perturbations is above the Higuchi bound.