Noether symmetry in $f(R)$ cosmology

TL;DR

This paper explores Noether symmetries in $f(R)$ cosmology, identifying specific forms of $f(R)$ that admit symmetries, leading to power-law expansion and potential explanations for cosmic acceleration.

Contribution

The study explicitly determines the form of $f(R)$ functions compatible with Noether symmetries, linking symmetry properties to cosmological dynamics and dark energy alternatives.

Findings

Identified $f(R)$ forms with Noether symmetries.

Derived power-law expansion for the scale factor.

Proposed $f(R)$ models as gravitational alternatives to quintessence.

Abstract

The Noether symmetry of a generic $f(R)$ cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generators of the desired symmetry. We explicitly calculate the form of $f(R)$ for which such symmetries exist. It is shown that the resulting form of $f(R)$ yields a power law expansion for the cosmological scale factor. We also obtain the effective equation of state parameter for the corresponding cosmology and show that our model can provide a gravitational alternative to the quintessence.