Mass-Varying Massive Gravity

TL;DR

This work addresses making the graviton mass time- and space-dependent while remaining free of the Boulware-Deser ghost. It constructs a scalar-dRGT gravity with a graviton mass controlled by a scalar via $V(\psi)$ and demonstrates ghost-freedom through a Hamiltonian analysis that yields a Hamiltonian constraint $\mathcal{C}$ and a secondary constraint $\mathcal{C}^{(2)}$, with no tertiary constraint. The authors study homogeneous and isotropic cosmology in the Minkowski-fiducial setup, deriving FRW equations for flat and open geometries and identifying a special integrable branch that reduces to General Relativity plus a scalar with an effective potential $\bar{W}(\psi)=W(\psi)-\frac{4}{\alpha_3^{2}}V(\psi)$; they discuss a concrete inflation-to-dark-energy scenario where the graviton mass evolves from a high to a low scale. The results provide a ghost-free, dynamically rich framework that can link early-universe inflation to late-time acceleration via a evolving graviton mass, with potential generalizations including $\psi$-dependent parameters and non-minimal couplings.

Abstract

It has recently been shown that the graviton can consistently gain a constant mass without introducing the Boulware-Deser ghost. We propose a gravity model where the graviton mass is set by a scalar field and prove that this model is free of the Boulware-Deser ghost by analyzing its constraint system and showing that two constraints arise. We also initiate the study of the model's cosmic background evolution and tentatively discuss possible cosmological implications of this model. In particular, we consider a simple scenario where the scalar field setting the graviton mass is identified with the inflaton and the graviton mass evolves from a high to a low energy scale, giving rise to the current cosmic acceleration.