Evidence for and Obstructions to Non-Linear Partially Massless Gravity

TL;DR

This paper investigates the possibility of non-linear partially massless gravity, which could address the cosmological constant problem, but finds significant theoretical obstructions in existing models preventing its realization.

Contribution

The study critically examines known ghost-free massive gravity models and identifies key obstructions to formulating a non-linear partially massless gravity theory.

Findings

Strong evidence supports the existence of a PM gravity theory.

Technical obstructions prevent its formulation in standard frameworks.

The results highlight challenges in achieving non-linear PM gravity.

Abstract

Non-linear partially massless (PM) gravity, if it exists, is a theory of massive gravity in which the graviton has four propagating degrees of freedom. In PM gravity, a scalar gauge symmetry removes one of the five modes of the massive graviton. This symmetry ties the value of the cosmological constant to the mass of the graviton, which in turn can be kept small in a technically natural way. Thus PM gravity could offer a compelling solution to the old cosmological constant problem. In this work we look for such a theory among the known ghost-free massive gravity models with a de Sitter reference metric. We find that despite the existence of strong supporting evidence for the existence of a PM theory of gravity, technical obstructions arise which preclude its formulation using the standard massive gravity framework.