Completing Lorentz violating massive gravity at high energies

TL;DR

This paper constructs a high-energy ultraviolet completion for Lorentz-violating massive gravity, enabling consistent quantization and revealing novel gravitational phenomenology, including a repulsive potential at large distances.

Contribution

It introduces a high-energy consistent UV completion for massive gravity based on vector field condensation and Lorentz violation, extending the theory's validity beyond previous cutoffs.

Findings

The theory remains consistent up to a high energy scale independent of graviton mass.

Homogeneous cosmological solutions match standard cosmology.

Gravitational potential becomes repulsive at large distances.

Abstract

Theories with massive gravitons are interesting for a variety of physical applications, ranging from cosmological phenomena to holographic modeling of condensed matter systems. To date, they have been formulated as effective field theories with a cutoff proportional to a positive power of the graviton mass m_g and much smaller than that of the massless theory (M_P ~ 10^19 GeV in the case of general relativity). In this paper we present an ultraviolet completion for massive gravity valid up to a high energy scale independent of the graviton mass. The construction is based on the existence of a preferred time foliation combined with spontaneous condensation of vector fields. The perturbations of these fields are massive and below their mass the theory reduces to a model of Lorentz violating massive gravity. The latter theory possesses instantaneous modes whose consistent quantization we discuss in detail. We briefly study some modifications to gravitational phenomenology at low-energies. The homogeneous cosmological solutions are the same as in the standard cosmology. The gravitational potential of point sources agrees with the Newtonian one at distances small with respect to m_g^(-1). Interestingly, it becomes repulsive at larger distances.