Lorentz Breaking Massive Gravity in Curved Space

TL;DR

This paper explores the behavior of Lorentz-breaking massive gravity in curved spacetimes, revealing conditions for stability, phase structures, and modifications to gravitational potentials, with implications for cosmology and gravity theories.

Contribution

It extends the analysis of Lorentz-breaking massive gravity to curved backgrounds, including FRW, and investigates stability, degrees of freedom, and gravitational potential modifications.

Findings

Ghost instabilities are avoidable in FRW backgrounds.

The Higuchi bound is extended to FRW with Lorentz breaking.

Gravitational potentials match GR at small scales, with modifications at larger distances.

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.