Gravitational- and Self- Coupling of Partially Massless Spin 2

TL;DR

The paper addresses whether partially massless spin-2 fields can propagate and interact nonlinearly in cosmological spacetimes. It uses conformal Weyl gravity as a controlled framework to examine PM propagation and possible nonlinearities, identifying background restrictions and the nature of self-couplings. The authors show that PM propagation is only consistent on Einstein backgrounds and that, within CG, the only ghost-free self-interaction is the cubic Noether-current coupling; nonlinear truncations to PM gravity are not possible in four dimensions. These results reinforce the view that PM theories face strong consistency constraints, while suggesting directions for cosmological applications and higher-spin conformal gravity generalizations.

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.