To the Problem of Cosmic Expansion in Massive Gravity

TL;DR

This paper classifies and analyzes cosmological solutions in ghost-free massive gravity, showing that dynamical FLRW backgrounds require inhomogeneous or anisotropic Stueckelberg fields and that perturbations are strongly coupled.

Contribution

It provides a new classification of flat FLRW solutions in dRGT massive gravity by relaxing assumptions on Stueckelberg fields and characterizes their properties.

Findings

Dynamical solutions require inhomogeneous or anisotropic Stueckelberg profiles.

Perturbations are strongly coupled at quadratic order on these backgrounds.

No dynamical flat FLRW background exists with Minkowski reference metric under standard assumptions.

Abstract

We consider evolving, spatially flat isotropic and homogeneous (FLRW) cosmologies in ghost-free (dRGT) massive gravity. In this theory, no dynamical flat FLRW background exists if the reference metric is chosen to be Minkowski and the Stueckelberg fields are homogeneous. Relaxing the assumptions on the Stueckelberg profiles gives access to dynamical backgrounds. We propose a classification of the viable flat FLRW cosmological solutions of dRGT massive gravity. Instead of specifying an initial ansatz for the Stueckelberg fields $\phi^a$ and the reference metric $f_{ab}$, we show that imposing homogeneity and isotropy on the square root tensor $X^{\mu}_{\nu}=\left(\sqrt{g^{-1}\partial\phi^a \partial\phi^bf_{ab}}\right)^{\mu}_{\nu}$ leads to dynamical cosmological solutions, and we characterize their properties. These solutions become dynamical only when the Stueckelberg fields acquire a sufficiently inhomogeneous and/or anisotropic profile. We explore the consequences for the minimal model and the complete dRGT theory, and show that perturbations are strongly coupled, at the quadratic level, on these backgrounds.