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

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

2008-09-26

arxiv.org/abs/0809.4591v1

Phys.Lett.B669:206-211,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, 1 figure, to appear in PLB

Scientific paper

10.1016/j.physletb.2008.09.058

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.

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