On massive higher spins and gravity. Part II. Spin 3

A bstract In this paper, we continue our investigation of gravitational interactions for massive higher spins, extending our recent work on massive spin 5/2 to massive spin 3, including its massless and partially massless limits. To construct the minimal gravitational interactions (i.e. vertexes containing both standard minimal interactions and non-minimal ones, which are necessary for any s ≥ 5/2), we use a gauge invariant frame-like formalism. Similarly to the spin 5/2 case, there is a special point m 2 = 6Λ, which corresponds to a boundary of the unitary allowed region in dS 4 , where minimal interactions disappear, leaving only the non-minimal ones.