Theoretical Aspects of Massive Gravity

TL;DR

This paper reviews the theoretical developments in massive gravity, including historical challenges, modern effective field theory approaches, and recent progress addressing key issues like the vDVZ discontinuity and ghost problems.

Contribution

It provides a comprehensive pedagogical review of massive gravity's theoretical aspects, including new insights into effective field theories and mechanisms resolving classical issues.

Findings

Re-derivation of vDVZ discontinuity and Boulware-Deser ghost

Discussion of Vainshtein screening mechanism

Identification of interactions raising EFT cutoff and removing ghosts

Abstract

Massive gravity has seen a resurgence of interest due to recent progress which has overcome its traditional problems, yielding an avenue for addressing important open questions such as the cosmological constant naturalness problem. The possibility of a massive graviton has been studied on and off for the past 70 years. During this time, curiosities such as the vDVZ discontinuity and the Boulware-Deser ghost were uncovered. We re-derive these results in a pedagogical manner, and develop the St\"ukelberg formalism to discuss them from the modern effective field theory viewpoint. We review recent progress of the last decade, including the dissolution of the vDVZ discontinuity via the Vainshtein screening mechanism, the existence of a consistent effective field theory with a stable hierarchy between the graviton mass and the cutoff, and the existence of particular interactions which raise the maximal effective field theory cutoff and remove the ghosts. In addition, we review some peculiarities of massive gravitons on curved space, novel theories in three dimensions, and examples of the emergence of a massive graviton from extra-dimensions and brane worlds.