Revisiting conserved currents in F(R) theory of gravity via Noether symmetry

TL;DR

This paper clarifies the conserved currents in F(R) gravity using Noether symmetry, demonstrating that previous claims of multiple conserved currents are incorrect and that only one fundamental conserved current exists.

Contribution

The paper critically analyzes prior claims of multiple conserved currents in F(R) gravity and establishes that only one conserved current is valid, clarifying the role of Noether symmetry.

Findings

Only one conserved current exists in F(R) gravity under Noether symmetry.

Previous claims of multiple conserved currents are shown to be incorrect.

The conserved current is /dt(a R) in Robertson-Walker metric.

Abstract

Noether symmetry of F(R) theory of gravity in vacuum and in the presence of pressureless dust yields F(R) \propto R^{3/2} along with the conserved current \frac{d}{dt}(a\sqrt R) in Robertson-Walker metric and nothing else. Still some authors recently claimed to have obtained four conserved currents setting F(R) \propto R^{3/2} a-priori, taking time translation along with a gauge term. We show that the first one of these does not satisfy the field equations and the second one is the Hamiltonian which is constrained to vanish in gravity and thus a part and parcel of the field equations. We also show that the other two conserved currents, which do not contain time translation are the same in disguise and identical to the one mentioned above. Thus the claim is wrong.