Conserved Quantities in f ( R ) Gravity via Noether Symmetry

Abstract

We investigate 𝑓 (𝑅) gravity using the 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 the gauge term. Further, we calculate the corresponding conserved quantities in each case. Moreover, the importance and stability criteria of these models are discussed.

Noether symmetry analysis of anisotropic universe in modified gravity

“…The results in this regard agree with [27] for special cases when m = 1. More importantly we have also recovered the Noether symmetries for f (R) and f (G) theories of gravity and the results agree with [21,45] for f (R) gravity.…”

“…and the results agree with [21,45]. To recover the Noether symmetries in f (G) gravity we choose f (R,…”

Scalar tensor teleparallel dark gravity via Noether symmetry

“…We also note that the Noether symmetry approach allows one to choose the potential dynamically in the scalar-tensor gravity theory [56][57][58][59][60][61][62][63][64], and the explicit form of the function f (R) of the modified f (R) theories of gravity [65][66][67][68][69][70][71]. In this form of f (R), cosmological solutions in the case of FRW metric can describe the accelerated period of the Universe.…”

Cosmological analysis of scalar field models in f(R, T) gravity

“…Capozziello et al [18] used this approach to find exact solutions of spherically symmetric spacetime in f (R) gravity. Hussain et al [19] investigated the existence of Noether symmetry of a power-law f (R) model and found the boundary term to vanish for the flat FRW universe model but Shamir et al [20] obtained a non-zero boundary term of the same model. Momeni et al [21] explored a Noether point symmetry of the isotropic universe in mimetic f (R) and f (R, T ) gravity theories.…”