Universally Coupled Massive Gravity, II: Densitized Tetrad and Cotetrad Theories

TL;DR

This paper develops new massive gravity theories using tetrad formulations, allowing flexible mass relationships between spin 0 and spin 2 components, with potential applications in astrophysics and cosmology.

Contribution

It introduces universally coupled massive tetrad gravity theories derived from a linear flat spacetime framework, expanding the class of viable models with adjustable spin 0 and spin 2 masses.

Findings

Two one-parameter families of massive gravity theories identified.

Theories include both covariant and contravariant potentials with various density weights.

Mass of spin 0 can be heavier, lighter, or equal to spin 2, offering phenomenological flexibility.

Abstract

Einstein's equations in a tetrad formulation are derived from a linear theory in flat spacetime with an asymmetric potential using free field gauge invariance, local Lorentz invariance and universal coupling. The gravitational potential can be either covariant or contravariant and of almost any density weight. These results are adapted to produce universally coupled massive variants of Einstein's equations, yielding two one-parameter families of distinct theories with spin 2 and spin 0. The theories derived, upon fixing the local Lorentz gauge freedom, are seen to be a subset of those found by Ogievetsky and Polubarinov some time ago using a spin limitation principle. In view of the stability question for massive gravities, the proven non-necessity of positive energy for stability in applied mathematics in some contexts is recalled. Massive tetrad gravities permit the mass of the spin 0 to be heavier than that of the spin 2, as well as lighter than or equal to it, and so provide phenomenological flexibility that might be of astrophysical or cosmological use.