Gravitational- and Self- Coupling of Partially Massless Spin 2

TL;DR

This paper investigates the challenges in coupling partially massless spin 2 fields to gravity, revealing limitations in nonlinear extensions and identifying safe self-couplings within conformal Weyl gravity.

Contribution

It demonstrates that partially massless spin 2 fields face coupling issues similar to other higher spin systems and identifies consistent self-couplings using conformal Weyl gravity.

Findings

Coupling problems persist beyond Einstein backgrounds.

Nonlinear extensions suffer from background- and self-coupling difficulties.

Safe self-couplings are limited to Noether current cubic interactions.

Abstract

We show that higher spin systems specific to cosmological spaces are subject to the same problems as models with Poincar'e limits. In particular, we analyse partially massless (PM) spin 2 and find that both its gravitational coupling and nonlinear extensions suffer from the usual [background- and self-coupling] difficulties: Consistent free field propagation does not extend beyond background Einstein geometries. Then, using conformal Weyl gravity (CG), which consists of relative ghost PM and graviton excitations, we find that avoiding graviton-ghosts restricts CG-generated PM self-couplings to the usual, safe, Noether current cubic ones.