A non-linear extension of the spin-2 partially massless symmetry

TL;DR

This paper explores extending the partially massless symmetry of a spin-2 field in de Sitter space to nonlinear order, finding a unique symmetry but no compatible low-derivative Lagrangian.

Contribution

It identifies a unique nonlinear extension of the free partially massless symmetry and demonstrates the absence of a suitable low-derivative Lagrangian.

Findings

Unique nonlinear symmetry extension found.

No consistent two-derivative Lagrangian exists for this symmetry.

Constraints strongly limit nonlinear partially massless theories.

Abstract

We investigate the possibility of extending the "partially massless" symmetry of a spin-2 field in de Sitter to nonlinear order. To do so, we impose a closure condition on the symmetry transformations. This requirement imposes strong constraints on the form of the nonlinear symmetry while making only minimal assumptions about the form of the nonlinear partially massless action. We find a unique nonlinear extension of the free partially massless symmetry. However, we show that no consistent Lagrangian that contains at most two derivatives of the fields can realize this symmetry.