Description
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 (some, but not
all, with vanishing Bach tensors) allowing for the propagation of a
partially massless graviton. These include in particular the Einstein
static Universe.