Universally Coupled Massive Gravity

TL;DR

This paper derives Einstein's equations from a linear flat-space theory, extends them to massive variants with spin 2 and 0, and explores the uniqueness and properties of these theories, including energy and causality issues.

Contribution

It introduces new universally coupled massive gravity theories, expanding beyond the known Freund-Maheshwari-Schonberg model, and connects them to prior work by Ogievetsky and Polubarinov.

Findings

Derived Einstein's equations from linear gauge-invariant theories.

Constructed two-parameter families of massive gravity theories.

Discussed energy positivity and causality concerns in these theories.

Abstract

We derive Einstein's equations from a linear theory in flat space-time using free-field gauge invariance and universal coupling. The gravitational potential can be either covariant or contravariant and of almost any density weight. We adapt these results to yield universally coupled massive variants of Einstein's equations, yielding two one-parameter families of distinct theories with spin 2 and spin 0. The Freund-Maheshwari-Schonberg theory is therefore not the unique universally coupled massive generalization of Einstein's theory, although it is privileged in some respects. The theories we derive are a subset of those found by Ogievetsky and Polubarinov by other means. The question of positive energy, which continues to be discussed, might be addressed numerically in spherical symmetry. We briefly comment on the issue of causality with two observable metrics and the need for gauge freedom and address some criticisms by Padmanabhan of field derivations of Einstein-like equations along the way.