On massive higher spins and gravity. II. Spin 3

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 $s \ge 5/2$), we use a gauge invariant frame-like formalism. Similarly to the spin 5/2 case, there is a special point $m^2 = 6\Lambda$, which corresponds to a boundary of the unitary allowed region in $dS_4$, where minimal interactions disappear, leaving only the non-minimal ones.