  Some time ago, we showed that a weak (linear) massless spin 2 wave could only
propagate on a Ricci-flat or Ricci-constant background: it must necessarily be
a perturbation of General Relativity. This was just the continuation of the
higher spin chain: massless $s=3/2$ also required Ricci-flatness (which is the
basis of supergravity) while $s>2$ needs Riemann flatness. This note
re-analyzes the problem in a perhaps more physical way: by considering massless
and -- only apparently -- massive small excitations and showing how their
parameters relate to the cosmological constant. We will thus prove, in a simple
physical way, the necessity, as well as the sufficiency, of the known
supergravity results.
