Nonlinear Partially Massless from Massive Gravity?

TL;DR

This paper investigates whether nonlinear partially massless gravity can emerge from f–g massive gravity on de Sitter-like backgrounds. Through a detailed constraint analysis, it constructs a putative PM model and shows that the necessary Bianchi identity does not materialize at nonlinear order, eliminating nonlinear PM in this framework. It further demonstrates that the familiar five-DoF f–g models are generically acausal, implying that PM-inspired extensions are not physically viable here. Overall, the work rules out nonlinear PM in ghost-free f–g theories and connects PM obstructions to persistent acausality concerns in these models.

Abstract

We show that consistent nonlinear Partially Massless models cannot be obtained starting from "f-g" massive gravity, with "f" the embedding de Sitter space. The obstruction, which is also the source of f-g acausality, is the very same fifth constraint that removes the notorious sixth ghost excitation. Here, however, it blocks extension of the mass to cosmological background tuned gauge invariance that took away the helicity zero mode at linear level. Separately, our methods allow us to almost complete the class of acausal f-g models.