Self-accelerating Massive Gravity: Exact solutions for any isotropic matter distribution

TL;DR

The paper investigates whether a massive graviton can drive cosmic acceleration without conventional dark energy by deriving exact isotropic solutions in the ghost-free dRGT massive gravity framework. By solving for the Stückelberg field configurations and using a Cayley-Hamilton approach, it finds an exact solution with $g = x_0 a r$ and $P_1(x_0)=0$, yielding a constant effective stress-energy $\rho_{\mathcal{K}} = -p_{\mathcal{K}} = \frac{1}{2} m^2 M_{\rm pl}^2 P_0(x_0)$. Consequently, the modified Einstein equations take the form $G_{\mu\nu} = m^2 T^{(\mathcal{K})}_{\mu\nu} + \frac{1}{M_{\rm pl}^2} T^{(m)}_{\mu\nu}$, i.e., GR with a cosmological-constant-like term for general isotropic matter, including FRW cosmologies and perturbations around them. The solution subsumes known vacuum cases (e.g., Schwarzschild–de Sitter) and connects flat matter-dominated histories to self-accelerating expansion, while raising questions about perturbation kinetic terms on this background.

Abstract

We present an exact solution to the equations of massive gravity that displays cosmological constant-like behavior for any spherically symmetric distribution of matter, including arbitrary time dependence. On this solution, the new degrees of freedom from the massive graviton generate a cosmological constant-like contribution to stress-energy that does not interact directly with other matter sources. When the effective cosmological constant contribution dominates over other sources of stress energy the cosmological expansion self-accelerates, even when no other dark-energy-like ingredients are present. The new degrees of freedom introduced by giving the graviton the mass do not respond to arbitrarily large radial or homogeneous perturbations from other matter fields on this solution. We comment on possible implications of this result.