Resolving Puzzles of Massive Gravity with and without violation of Lorentz symmetry

TL;DR

This paper systematically studies various massive gravity theories with and without Lorentz symmetry violation, revealing their peculiar properties, instabilities, and potential healthy models involving infinite extra fields, especially in higher-dimensional frameworks.

Contribution

It provides a comprehensive analysis of massive gravity models, identifying their unusual features, instabilities, and proposing that healthy models may involve infinite Kaluza-Klein towers of fields.

Findings

Unusual properties due to mixing of fields and non-trivial dispersion laws.

Presence of superluminal propagation, ghosts, and tachyons in these theories.

Healthy models may require infinite extra fields, like Kaluza-Klein towers.

Abstract

We perform a systematic study of various versions of massive gravity with and without violation of Lorentz symmetry in arbitrary dimension. These theories are well known to possess very unusual properties, unfamiliar from studies of gauge and Lorentz invariant models. These peculiarities are caused by mixing of familiar transverse fields with revived longitudinal and pure gauge (Stueckelberg) fields and are all seen already in quadratic approximation. They are all associated with non-trivial dispersion laws, which easily allow superluminal propagation, ghosts, tachyons and essential irrationalities. Moreover, coefficients in front of emerging modes are small, what makes the theories essentially non-perturbative within a large Vainshtein radius. Attempts to get rid of unwanted degrees of freedom by giving them infinite masses lead to DVZ discontinuities in parameter (moduli) space, caused by un-permutability of different limits. Also, the condition m_{gh}=\infty can not be preserved already in non-trivial gravitational backgrounds and is unstable under any other perturbations of linearized gravity. At the same time an {\it a priori} healthy model of massive gravity in quadratic approximation definitely exists: provided by any mass level of Kaluza-Klein tower. It bypasses the problems because gravity field is mixed with other fields, and this explains why such mixing helps in other models. At the same time this can imply that the really healthy massive gravity can still require infinite number of extra fields beyond quadratic approximation.