Lorentz Breaking Massive Gravity in Curved Space

TL;DR

This work analyzes Lorentz-breaking massive gravity on curved FRW backgrounds, decomposing perturbations into tensor, vector, and scalar sectors with time-dependent LB mass terms $m_i( au)$. It finds that tensors and vectors largely mirror Minkowski behavior, but the scalar sector generically hosts two propagating DOF; crucially, FRW curvature can remove ghost-like instabilities that arise in maximally symmetric spaces, and the Higuchi bound is extended to FRW contexts. The study reveals multiple phases with either two or fewer scalar DOF, including partially massless and FP-like limits, and demonstrates that curvature can regulate infrared modifications so GR is recovered at short distances while allowing controlled deviations at large scales. The results inform the viability of IR modifications of gravity, reveal potential strong-coupling issues in some regimes, and suggest further exploration of non-linear effects and cosmological/astrophysical phenomenology.

Abstract

A systematic study of the different phases of Lorentz-breaking massive gravity in a curved background is performed. For tensor and vector modes, the analysis is very close to that of Minkowski space. The most interesting results are in the scalar sector where, generically, there are two propagating degrees of freedom (DOF). While in maximally symmetric spaces ghost-like instabilities are inevitable, they can be avoided in a FRW background. The phases with less than two DOF in the scalar sector are also studied. Curvature allows an interesting interplay with the mass parameters; in particular, we have extended the Higuchi bound of dS to FRW and Lorentz breaking masses. As in dS, when the bound is saturated there is no propagating DOF in the scalar sector. In a number of phases the smallness of the kinetic terms gives rise to strongly coupled scalar modes at low energies. Finally, we have computed the gravitational potentials for point-like sources. In the general case we recover the GR predictions at small distances, whereas the modifications appear at distances of the order of the characteristic mass scale. In contrast with Minkowski space, these corrections may not spoil the linear approximation at large distances.