Improved Positivity Bounds and Massive Gravity

TL;DR

This paper examines how improved positivity bounds impact massive gravity theories, showing they are compatible with weak coupling and do not rule out such models, but imply a lower EFT cutoff.

Contribution

It provides a detailed analysis of the EFT Lagrangian for massive gravity, aligning it with massive Galileons, and clarifies the implications of positivity bounds on the theory's cutoff.

Findings

Positivity bounds are compatible with weakly coupled massive gravity.

The EFT cutoff is lower than previously assumed due to improved bounds.

Vainshtein mechanism remains consistent with weak coupling.

Abstract

Theories such as massive Galileons and massive gravity can satisfy the presently known improved positivity bounds provided they are weakly coupled. We discuss the form of the EFT Lagrangian for a weakly coupled UV completion of massive gravity which closely parallels the massive Galileon, and perform the power counting of corrections to the scattering amplitude and the positivity bounds. The Vainshtein mechanism which is central to the phenomenological viability of massive gravity is entirely consistent with weak coupling since it is classical in nature. We highlight that the only implication of the improved positivity constraints is that EFT cutoff is lower than previous assumed, and discuss the observable implications, emphasizing that these bounds are not capable of ruling out the model contrary to previous statements in the literature.