Revisiting Noether gauge symmetry for F(R) theory of gravity

Abstract

Noether gauge symmetry for F(R) theory of gravity has been explored recently. The fallacy is that, even after setting gauge to vanish, the form of F(R) \propto R^n (where n \neq 1, is arbitrary) obtained in the process, has been claimed to be an outcome of gauge Noether symmetry. On the contrary, earlier works proved that any nonlinear form other than F(R) \propto R^3/2 is obscure. Here, we show that, setting gauge term zero, Noether equations are satisfied only for n = 2, which again does not satisfy the field equations. Thus, as noticed earlier, the only admissible form that Noether symmetry is F(R) \propto R^3/2 . Noether symmetry with non-zero gauge has also been studied explicitly here, to show that it does not produce anything new.

9 pages, To appear in Astrophysics Space Science

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• A viable form of the metric Teleparallel F(T) theory of gravity
• Using Noether symmetries to specify f(R) 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
• Symmetries of Differential equations and Applications in Relativistic Physics
• Reconstructing modified and alternative theories of gravity
• Analyzing Conserved Currents in F(R) theory of gravity
• Revisiting Noether symmetry approach in F(R)-tachyon Model