Quadratic quantum cosmology with Schutz' perfect fluid

We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology coupled to a perfect fluid in the context of f(R) gravity. We use the Schutz ’ variational formalism for the perfect fluid and show that it leads to a time parameter for the corresponding dynamical system. This formalism gives rise to a Schrödinger-Wheeler-DeWitt (SWD) equation for the quantum cosmology of the model where its eigenfunctions can be used to construct the wavefunction of the universe. In the case of f(R) = R 2 (pure quadratic model), for some special perfect fluids the exact solutions of SWD equation are obtained and the results are compared with the usual f(R) = R model. PACS numbers: 98.80.Qc, 04.50.+h, 04.60.Ds 1