# Partially Massless Graviton on Beyond Einstein Spacetimes

## TL;DR

This paper demonstrates that partially massless gravitons can exist on a broad class of non-Einstein spacetimes, expanding the understanding of their propagation beyond previously known Einstein backgrounds.

## Contribution

It provides explicit conditions and examples for the existence of partially massless gravitons on non-Einstein, Ricci symmetric spacetimes, based on a recently developed massive gravity theory.

## Key findings

- Partially massless gravitons can propagate on non-Einstein spacetimes.
- Explicit conditions for the scalar constraint to be satisfied are derived.
- Examples of non-Einstein, Ricci symmetric spacetimes supporting partial masslessness are provided.

## Abstract

We show that a partially massless graviton can propagate on a large set of spacetimes which are not Einstein spacetimes. Starting from a recently constructed theory for a massive graviton that propagates the correct number of degrees of freedom on an arbitrary spacetime, we first give the full explicit form of the scalar constraint responsible for the absence of a sixth degree of freedom. We then spell out generic conditions for the constraint to be identically satisfied, so that there is a scalar gauge symmetry which makes the graviton partially massless. These simplify if one assumes that spacetime is Ricci symmetric. Under this assumption, we find explicit non-Einstein spacetimes allowing for the propagation of a partially massless graviton.