Noether symmetric f (R) quantum cosmology and its classical correlations

We quantize a flat FRW cosmology in the context of the f (R) gravity by Noether symmetry approach. We explicitly calculate the form of f (R) for which such symmetries exist. It is shown that the existence of a Noether symmetry yields a general solution of the Wheeler-DeWitt equation where can be expressed as a superposition of states of the form e(iS). In terms of Hartle criterion, this type of wave function exhibits classical correlations, i.e. the emergent of classical universe is expected due to the oscillating behavior of the solutions of Wheeler-DeWitt equation. According to this interpretation we also provide the Noether symmetric classical solutions of our f (R) cosmological model. (C) 2008 Elsevier B.V. All rights reserved.