Positivity Constraints for Pseudo-linear Massive Spin-2 and Vector Galileons

TL;DR

This paper derives analyticity constraints on ghost-free effective theories of massive spin-2 and spin-1 particles, revealing limitations of certain models like pseudo-linear massive gravity and conditions for vector Galileons.

Contribution

It provides the first analytical positivity constraints on pseudo-linear massive gravity and explores the compatibility of higher derivative vector Galileon actions with positivity.

Findings

No parameter window satisfies constraints for pseudo-linear massive gravity.

Two-derivative vector Galileon actions are incompatible with positivity.

Higher derivative vector Galileon actions can satisfy positivity constraints.

Abstract

We derive analyticity constraints on a nonlinear ghost-free effective theory of a massive spin-2 particle known as pseudo-linear massive gravity, and on a generalized theory of a massive spin-1 particle, both of which provide simple IR completions of Galileon theories. For pseudo-linear massive gravity we find that, unlike dRGT massive gravity, there is no window of parameter space which satisfies the analyticity constraints. For massive vectors which reduce to Galileons in the decoupling limit, we find that no two-derivative actions are compatible with positivity, but that higher derivative actions can be made compatible.