A note on spin two fields in curved backgrounds

TL;DR

This paper revisits the constraints on massless spin-2 fields in curved backgrounds, confirming they must correspond to linear deviations from Einstein gravity, unaffected by non-minimal or non-analytic modifications.

Contribution

It demonstrates the uniqueness of the Einstein gravity linear deviation as the consistent description of massless spin-2 fields in curved backgrounds, despite various modifications.

Findings

Massless spin-2 fields must be linear deviations of Einstein gravity.

Non-minimal higher derivative terms do not alter this requirement.

Allowing non-analytic terms in the cosmological constant does not change the conclusion.

Abstract

We reconsider the consistency constraints on a free massless symmetric, rank 2, tensor field in a background and confirm that they uniquely require it to be the linear deviation about (cosmological) Einstein gravity. Neither adding non-minimal higher derivative terms nor changing the gauge transformations by allowing terms non-analytic in the cosmological constant alters this fact.