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

TL;DR

This paper applies Noether symmetry to quantize flat FRW cosmology within $f(R)$ gravity, deriving specific forms of $f(R)$, solving the Wheeler-DeWitt equation, and showing how classical universe behavior emerges from quantum states.

Contribution

It introduces a method to identify $f(R)$ functions with Noether symmetries and links quantum solutions to classical cosmological behavior.

Findings

Derived specific $f(R)$ forms with Noether symmetry.

Obtained solutions to the Wheeler-DeWitt equation as superpositions of oscillatory states.

Demonstrated classical correlations emerge from quantum wave functions.

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 $e^{iS}$. 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.