On massive gravity and bigravity in three dimensions

TL;DR

This paper explores consistent models of massive spin 2 particles in three dimensions, using a gauge-invariant approach, and identifies solutions that extend to non-linear regimes, including a form of 'New massive gravity.'

Contribution

It provides the most general linear approximations for massive spin 2 models in 3D and demonstrates the existence of non-linear solutions with a smooth massless limit.

Findings

Constructed the most general cubic vertices for massive spin 2 in 3D.

Identified at least one non-linear solution with a non-singular massless limit.

Connected the findings to 'New massive gravity' models.

Abstract

In this paper we investigate possible consistent ghost-free models containing massive spin 2 particles in three dimensions. We work in a constructive approach based on the frame-like gauge invariant description for such massive spin 2 particles. We provide the most general form of linear approximations, i.e. cubic vertices in the Lagrangian and linear in fields corrections to gauge transformations. As for the possibility to go beyond the linear approximation, we show that there exists at least one solution that admits non-singular massless limit and that corresponds to a so called "New massive gravity".