Revisiting Conserved Currents in the F(R) Theory of Gravity via Noether Symmetry

Noether symmetry of the F(R) theory of gravity in a vacuum and in the presence of pressureless dust yields F(R)∝R^3/2 along with the conserved current d/dt(a√R) in the Robertson–Walker metric and nothing else. However, some authors recently claimed to have obtained four conserved currents setting F(R)∝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.