Auxiliary "massless" spin-2 field in de Sitter universe

For the tensor field of rank-2 there are two unitary irreducible representation (UIR) in de Sitter (dS) space denoted by $\Pi^{\pm}_{2,2}$ and $\Pi^{\pm}_{2,1}$ [1]. In the flat limit only the $\Pi^{\pm}_{2,2}$ coincides to the UIR of Poincar\'e group, the second one becomes important in the study of conformal gravity. In the pervious work, Dirac's six-cone formalism has been utilized to obtain conformally invariant (CI) field equation for the "massless" spin-2 field in dS space [2]. This equation results in a field which transformed according to $\Pi^{\pm}_{2,1}$, we name this field the auxiliary field. In this paper this auxiliary field is considered and also related two-point function is calculated as a product of a polarization tensor and "massless" conformally coupled scalar field. This two-point function is de Sitter invariant.