Exact self-accelerating cosmologies in the ghost-free massive gravity -- the detailed derivation

TL;DR

This paper provides a detailed derivation of the most general homogeneous and isotropic cosmological solutions in ghost-free massive gravity, demonstrating their properties and potential implications for late-time cosmic acceleration.

Contribution

It offers a comprehensive derivation of the general cosmological solutions in ghost-free massive gravity, including matter and various spatial curvatures, using both matrix square root and tetrad formalisms.

Findings

Solutions include matter sources and various spatial curvatures.

The solutions exhibit late-time acceleration due to the graviton mass.

Inhomogeneous St"uckelberg fields may lead to perturbations, suppressed by small graviton mass.

Abstract

We present the detailed derivation of the recently announced most general cosmological solution with homogeneous and isotropic metric in the ghost-free massive gravity theory. We use the standard parametrization of the theory in terms of the matrix square root, and then show how the same results are recovered within the tetrad formulation. The solution obtained includes the matter source, it exists for generic values of the theory parameters, and it describes a universe that can be spatially open, closed, or flat, and that shows the late time acceleration due to the effective cosmological term mimicked by the graviton mass. The St\"uckelberg fields are inhomogeneous, which could probably give rise to inhomogeneous perturbations of the homogeneous and isotropic backgrounds, although this effect should be suppressed by the smallness of the graviton mass.