Partially Massless Gravity

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On de
Sitter space, there exists a special value for the mass of a graviton for which
the linear theory propagates 4 rather than 5 degrees of freedom. If a fully non-linear version of the theory
exists and can be coupled to known matter, it would have interesting properties
and could solve the cosmological constant problem. I will describe evidence for and obstructions
to the existence of such a theory.