Open FRW universes and self-acceleration from nonlinear massive gravity

TL;DR

This paper shows that nonlinear massive gravity with Lorentz-invariant mass terms admits open FRW cosmologies driven by arbitrary matter, contrasting with previous no-go results for flat FRW. By analyzing the Stückelberg sector, the authors identify three branches, two of which yield open FRW cosmologies whose Friedmann equation includes an effective cosmological constant $\Lambda_{\pm}=c_{\pm}m_g^2$, enabling self-acceleration for positive $c_{\pm}$. A crucial finding is the discontinuity at the flat FRW limit, since no exactly flat solution exists, though nearly flat open universes can approximate a flat FRW state. The results lay the groundwork for perturbation analyses on these open backgrounds and their potential observational signatures of massive gravity.

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 Stückelberg 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 $Λ_{\pm}=c_{\pm}m_g^2$. 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.