Constrained Dynamics of Universally Coupled Massive Spin 2-spin 0 Gravities

TL;DR

This paper applies the Dirac-Bergmann constrained dynamics analysis to a family of massive gravity theories, addressing their stability, causality, and energy properties, and extending understanding beyond linear approximations.

Contribution

It provides a detailed constrained dynamics analysis of universal coupling massive gravity theories, including the Freund-Maheshwari-Schonberg case, which was not previously examined at the nonlinear level.

Findings

Analysis of positive energy conditions

Causality issues addressed via gauge freedom

Extension of constrained dynamics to nonlinear massive gravities

Abstract

The 2-parameter family of massive variants of Einstein's gravity (on a Minkowski background) found by Ogievetsky and Polubarinov by excluding lower spins can also be derived using universal coupling. A Dirac-Bergmann constrained dynamics analysis seems not to have been presented for these theories, the Freund-Maheshwari-Schonberg special case, or any other massive gravity beyond the linear level treated by Marzban, Whiting and van Dam. Here the Dirac-Bergmann apparatus is applied to these theories. A few remarks are made on the question of positive energy. Being bimetric, massive gravities have a causality puzzle, but it appears soluble by the introduction and judicious use of gauge freedom.