Scale and Conformal Invariance on (A)dS

We examine the question of scale versus conformal invariance on maximally symmetric curved backgrounds and study general 2-derivative conformally invariant free theories of vectors and tensors. For spacetime dimension $D>4$, these conformal theories can be diagonalized into standard massive fields in which unbroken conformal symmetry non-trivially mixes components of different spins. In $D=4$, the tensor case becomes a conformal theory mixing a partially massless spin-2 field with a massless spin-1 field. For massless linearized gravity in $D=4$, we confirm through direct calculation that correlation functions of gauge-invariant operators take the conformally invariant form, despite the absence of standard conformal symmetry at the level of the action.