Nonlinear Dynamics of 3D Massive Gravity

TL;DR

This paper analyzes the nonlinear classical dynamics of 3D New Massive Gravity, demonstrating its consistency, the behavior of helicity-0 modes, and absence of ghost degrees of freedom, with generalizations to new models.

Contribution

It provides a detailed nonlinear analysis of 3D New Massive Gravity, revealing Galileon-like interactions and showing the theory's consistency without extra degrees of freedom.

Findings

Helicity-0 interactions described by cubic Galileon in decoupling limit

Conformal mode coincides with helicity-0 mode in this limit

No extra degrees of freedom or Boulware-Deser ghost present

Abstract

We explore the nonlinear classical dynamics of the three-dimensional theory of "New Massive Gravity" proposed by Bergshoeff, Hohm and Townsend. We find that the theory passes remarkably highly nontrivial consistency checks at the nonlinear level. In particular, we show that: (1) In the decoupling limit of the theory, the interactions of the helicity-0 mode are described by a single cubic term -- the so-called cubic Galileon -- previously found in the context of the DGP model and in certain 4D massive gravities. (2) The conformal mode of the metric coincides with the helicity-0 mode in the decoupling limit. Away from this limit the nonlinear dynamics of the former is described by a certain generalization of Galileon interactions, which like the Galileons themselves have a well-posed Cauchy problem. (3) We give a non-perturbative argument based on the presence of additional symmetries that the full theory does not lead to any extra degrees of freedom, suggesting that a 3D analog of the 4D Boulware-Deser ghost is not present in this theory. Last but not least, we generalize "New Massive Gravity" and construct a class of 3D cubic order massive models that retain the above properties.