  A frame work has been presented for theoretical interpretation of various
modified gravitational models which is based on the group theoretical approach
and unitary irreducible representations (UIR's) of de Sitter (dS) group. In
order to illustrate the application of the proposed method, a model of modified
gravity has been investigated. The background field method has been utilized
and the linearized modified gravitational field equation has been obtained in
the 4-dimensional dS space-time as the background. The field equation has been
written as the eigne-value equation of the Casimir operators of dS space using
the flat 5-dimensional ambient space notations. The Minkowskian correspondence
of the theory has been obtained by taking the zero curvature limit. It has been
shown that under some simple conditions, the linearized modified field equation
transforms 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 modified
gravitational theory can be a suitable one to describe the quantum
gravitational effects in its linear approximation on dS space. The field
equation has been solved and the solution has been written as the
multiplication of a symmetric rank-2 polarization tensor and a massless scalar
field using the ambient space notations. Also the two-point function has been
calculated in the ambient space formalism. It is dS invariant and free of any
theoretical problem.

General Relativity and Quantum Cosmology