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

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.

8 pages

References in corpus (6)

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• Physical non-equivalence of the Jordan and Einstein frames
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Cited by in corpus (4)

• Modified theory of gravity and the history of cosmic evolution
• Noether symmetry in $f(T)$ teleparallel gravity
• A viable form of the metric Teleparallel F(T) theory of gravity
• Analyzing Conserved Currents in F(R) theory of gravity