Anisotropic Friedmann-Robertson-Walker universe from nonlinear massive gravity

Abstract

In the scope of the nonlinear massive gravity, we study fixed points of evolution equations for a Bianchi type--I universe. We find a new attractor solution with non-vanishing anisotropy, on which the physical metric is isotropic but the Stuckelberg configuration is anisotropic. As a result, at the background level, the solution describes a homogeneous and isotropic universe, while a statistical anisotropy is expected from perturbations, suppressed by smallness of the graviton mass.

Figures (1)

• Figure 1: The phase flow for ($\sigma$, $\Sigma$) for parameters ($\alpha_3$, $\alpha_4$, $\lambda$, $\mu$) =($-0.05,\,1,\,0,\,20$). The flow is directed toward the red dot at ($\sigma$, $\Sigma$) = ($0.5$, $0$), which is the fixed point obtained by solving Eqs.(\ref{['eq1']})-(\ref{['eq3b']}).