Noether symmetric [formula omitted] quantum cosmology and its classical correlations

Babak Vakili

doi:10.1016/j.physletb.2008.09.058

Abstract

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 eiS. 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.

Highlights

In recent years, modified theories of gravity constructed by adding correction terms to the usual Einstein-Hilbert action, have opened a new window to study the accelerated expansion of the universe
In this letter we have studied a generic f (R) cosmological model by Noether symmetry approach
The phase space was constructed by taking the scale factor a and Ricci scalar R as the independent dynamical variables

Summary

Introduction

In recent years, modified theories of gravity constructed by adding correction terms to the usual Einstein-Hilbert action, have opened a new window to study the accelerated expansion of the universe. In the semiclassical approximation for the canonical quantum gravity, one can show that a wave function with classical correlations is a superposition of states of the form eiS, i.e. with oscillatory behavior [13] With this interpretation scheme for the solutions of Wheeler-DeWitt equation, we obtain the classical trajectory and show that the cosmological scale factor obeys a power law expansion. In an alternative approach to deal with quantum effects in the early universe one can use the idea of quantum field theory in curved space time [14] In this theory we assume that the matter fields are quantized while the gravitational field is classical and given by Einstein or any other modified gravity field equations. In [15] the role of quantum effects to the background cosmology at one-loop level are investigated in f (R) gravity framework

The Noether symmetric phase space of the model

Quantization of the model

Conclusions