Positive Signs in Massive Gravity

TL;DR

This paper derives new theoretical constraints on massive gravity theories using unitarity and analyticity principles, narrowing down the viable parameter space and resolving previous inconsistencies in scalar sector models.

Contribution

It provides the first comprehensive positivity bounds for general massive gravity, incorporating all polarization states and linking high-energy behavior to parameter constraints.

Findings

Excludes most of the parameter space for ghost-free massive gravity.

Shows consistency of full massive gravity theory with positivity constraints.

Identifies a small viable region in the parameter space.

Abstract

We derive new constraints on massive gravity from unitarity and analyticity of scattering amplitudes. Our results apply to a general effective theory defined by Einstein gravity plus the leading soft diffeomorphism-breaking corrections. We calculate scattering amplitudes for all combinations of tensor, vector, and scalar polarizations. The high-energy behavior of these amplitudes prescribes a specific choice of couplings that ameliorates the ultraviolet cutoff, in agreement with existing literature. We then derive consistency conditions from analytic dispersion relations, which dictate positivity of certain combinations of parameters appearing in the forward scattering amplitudes. These constraints exclude all but a small island in the parameter space of ghost-free massive gravity. While the theory of the "Galileon" scalar mode alone is known to be inconsistent with positivity constraints, this is remedied in the full massive gravity theory.