Improved Positivity Bounds and Massive Gravity

TL;DR

The paper examines improved positivity bounds for weakly coupled UV completions of massive Galileons and massive gravity, showing that these bounds constrain the EFT cutoff rather than ruling out the models. It develops a consistent framework where a single scale and small coupling, $\Lambda$ and $g_*$, describe the EFT, and where the Vainshtein mechanism remains classical and compatible with weak coupling through a background-dependent resummation that raises the effective cutoff to $\Lambda_c$. The analysis demonstrates that for realistic graviton masses (e.g., $m\sim H_0$), the required weak coupling $g_*$ is tiny, which keeps the theory within the positivity island and preserves phenomenological viability. The work also draws parallels with string-theoretic GR corrections, clarifies the role of higher-derivative operators in positivity bounds, and provides a detailed mapping between helicity-0 Galileon dynamics and massive gravity interactions, including a general treatment of helicity-0 and -1 identifications via Stückelberg fields.

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.