Linear higher order gravity in de sitter background

The field equation following the non-linear lagrangian -2λ+r+(alpha)r^(2)has been considered as an alternative to einstein's theory. based on the background field method, the linearized fourth order field equation has been obtained in both the 4-dimensional de sitter space-time and the flat 5-dimensional ambient space notations. the field equation has been projected into the minkowskian 4-dimensional space by taking the zero curvature limit. it has been shown that the field equation transforms according to one of the unitary irreducible representations of de sitter group denoted by (pi)(+-2,2)in discreet series.