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.

arXiv comment8 pages

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Cited by in corpus (8)

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• Modified theory of gravity and the history of cosmic evolution
• Studying the Intervention of an Unusual Term in $f(T)$ Gravity via Noether Symmetry
• Noether Symmetries of a Modified Model in Teleparallel Gravity and a New Approach for Exact Solutions
• A viable form of the metric Teleparallel F(T) theory of gravity
• Field independent cosmic evolution
• Late-time-accelerated expansion arisen from gauge fields in an anisotropic background and a fruitful trick for Noether's approach
• Analyzing Conserved Currents in F(R) theory of gravity