Massless Spin-2 Rank-3 Tensor Field in de Sitter Universe

From the conformal transformation, a massless spin-2 field must be presented by a rank-3 mixed symmetric tensor field. A massless spin-2 rank-3 mixed symmetric tensor field in de Sitter ambient space formalism is studied in this paper, which may be regarded as the linearized gravity or its dual. Recalling the field equation, the possible physical solutions of the field equation are calculated. The solutions can be written in terms of a rank-2 symmetric tensor field and a scalar field. We discuss that under what conditions this tensor field can be associated with the de Sitter and conformal groups unitary representations. Finally, for the physical solution, the quantum field operator and the two-point function are presented.