Conserved Quantities in $f(R)$ Gravity via Noether Symmetry

TL;DR

This paper explores $f(R)$ gravity models using Noether symmetry to identify conserved quantities, analyze specific cosmological and spherically symmetric solutions, and assess their stability.

Contribution

It applies the Noether symmetry approach to $f(R)$ gravity in FRW and spherical spacetimes, deriving conserved quantities and stability criteria for specific models.

Findings

Identified Noether symmetries for selected $f(R)$ models.

Derived conserved quantities associated with these symmetries.

Discussed stability conditions of the models.

Abstract

This paper is devoted to investigate $f(R)$ gravity using Noether symmetry approach. For this purpose, we consider Friedmann Robertson-Walker (FRW) universe and spherically symmetric spacetimes. The Noether symmetry generators are evaluated for some specific choice of $f(R)$ models in the presence of gauge term. Further, we calculate the corresponding conserved quantities in each case. Moreover, the importance and stability criteria of these models are discussed.