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 and (Dixmier in Bull Soc. Math. France 89:9, 1961 ). In the flat limit only the coincides to the UIR of Poincaré group, the second one becomes important in the study of conformal gravity. In the previous 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 (Dehghani et al. in Phys. Rev. D 77:064028, 2008 ). This equation results in a field which transformed according to , 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.