Propagation peculiarities of mean field massive gravity

TL;DR

This paper analyzes the propagation characteristics of mean field massive gravity, revealing superluminal behavior and hyperbolicity issues that limit its fundamental viability but suggest it may serve as an effective theory in weak regimes.

Contribution

It provides a detailed study of mean field massive gravity's propagation properties, highlighting superluminal modes and hyperbolicity constraints, connecting these features to analogous charged higher spin systems.

Findings

Hyperbolicity only holds in a weak background-mean-field limit.

Lower helicity modes exhibit superluminal propagation.

Both theories are limited to effective descriptions in weak regimes.

Abstract

Massive gravity (mGR) describes a dynamical "metric" on a fiducial, background one. We investigate fluctuations of the dynamics about mGR solutions, that is about its "mean field theory". Analyzing mean field massive gravity propagation characteristics is not only equivalent to studying those of the full non-linear theory, but also in direct correspondence with earlier analyses of charged higher spin systems, the oldest example being the charged, massive spin 3/2 Rarita--Schwinger (RS) theory. The fiducial and mGR mean field background metrics in the mean field mGR model correspond to the RS Minkowski metric and external EM field. The common implications in both systems are that hyperbolicity holds only in a weak background-mean-field limit, immediately ruling both theories out as fundamental theories. Although both can still be considered as predictive effective models in the weak regime, their lower helicities exhibit superluminal behavior: lower helicity gravitons are superluminal as compared to photons propagating on either the fiducial or background metric. This "crystal-like" phenomenon of differing helicities having differing propagation speeds in both mean field mGR and mGR is a peculiar feature of these models.