Open FRW universes and self-acceleration from nonlinear massive gravity

TL;DR

This paper explores open FRW universes within nonlinear massive gravity, revealing two solution branches that allow for self-accelerating cosmologies with an effective cosmological constant, but no exactly flat solutions exist.

Contribution

It identifies three solution branches in nonlinear massive gravity, two of which support open FRW universes with self-acceleration, extending previous no-go results for flat universes.

Findings

Two solution branches support open FRW universes with effective cosmological constants.

No exactly flat FRW solutions exist in the theory.

Open universes with small curvature approximate flat universes, showing a discontinuity at flat limit.

Abstract

In the context of a recently proposed nonlinear massive gravity with Lorentz-invariant mass terms, we investigate open Friedmann-Robertson-Walker (FRW) universes driven by arbitrary matter source. While the flat FRW solutions were recently shown to be absent, the proof does not extend to the open universes. We find three independent branches of solutions to the equations of motion for the St\"uckelberg scalars. One of the branches does not allow any nontrivial FRW cosmologies, as in the previous no-go result. On the other hand, both of the other two branches allow general open FRW universes governed by the Friedmann equation with the matter source, the standard curvature term and an effective cosmological constant $\Lambda_{\pm}=c_{\pm}m_g^2$. Here, $m_g$ is the graviton mass, +and - represent the two branches, and $c_{\pm}$ are constants determined by the two dimensionless parameters of the theory. Since an open FRW universe with a sufficiently small curvature constant can approximate a flat FRW universe but there is no exactly flat FRW solution, the theory exhibits a discontinuity at the flat FRW limit.