On massive gravity and bigravity in three dimensions

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 field corrections to gauge transformations. As for the possibility of going beyond the linear approximation, we show that there exists at least one solution that admits a non-singular massless limit and that corresponds to a so-called new massive gravity.