To the Problem of Cosmic Expansion in Massive Gravity

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.