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A frame work has been presented for theoretical interpretation of variousmodified gravitational models which is based on the group theoretical approachand unitary irreducible representations (UIR's) of de Sitter (dS) group. Inorder to illustrate the application of the proposed method, a model of modifiedgravity has been investigated. The background field method has been utilizedand the linearized modified gravitational field equation has been obtained inthe 4-dimensional dS space-time as the background. The field equation has beenwritten as the eigne-value equation of the Casimir operators of dS space usingthe flat 5-dimensional ambient space notations. The Minkowskian correspondenceof the theory has been obtained by taking the zero curvature limit. It has beenshown that under some simple conditions, the linearized modified field equationtransforms according to two of the UIR's of dS group labeled by $\Pi^\pm_{2,1}$and $\Pi^\pm_{2,2}$ in the discrete series. It means that the proposed modifiedgravitational theory can be a suitable one to describe the quantumgravitational effects in its linear approximation on dS space. The fieldequation has been solved and the solution has been written as themultiplication of a symmetric rank-2 polarization tensor and a massless scalarfield using the ambient space notations. Also the two-point function has beencalculated in the ambient space formalism. It is dS invariant and free of anytheoretical problem.

Group theoretical interpretation of the modified gravity in de Sitter space