Noether symmetric minisuperspace model of $f(R)$ cosmology

TL;DR

This paper uses Noether symmetry to identify specific $f(R)$ gravity models that admit power-law cosmological expansion and explores their quantum solutions, linking classical and quantum descriptions.

Contribution

It introduces a method to determine $f(R)$ functions with Noether symmetry in minisuperspace and analyzes their classical and quantum cosmological implications.

Findings

Identified $f(R)$ forms with Noether symmetry leading to power-law expansion.

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

Showed classical trajectories can be recovered from quantum wavefunctions.

Abstract

We study the metric $f(R)$ cosmology using Noether symmetry approach by utilizing the behavior of the corresponding Lagrangian under infinitesimal generators of the desired symmetry. The existence of Noether symmetry of the cosmological $f(R)$ minisuperspace helps us to find out the form of $f(R)$ function for which such symmetry exist. It is shown that the resulting form for $f(R)$ yields a power law expansion for the cosmic scale factor. We also show that in the corresponding Noether symmetric quantum model, the solutions to the Wheeler-DeWitt equation can be expressed as a superposition of states of the form $e^{iS}$. It is shown that in terms of such wavefunctions the classical trajectories can be recovered.