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

TL;DR

This paper critically examines the application of Noether gauge symmetry in F(R) gravity, clarifying that only the specific form F(R) ∝ R^{3/2} is consistent with the symmetry, challenging recent claims of more general solutions.

Contribution

The paper demonstrates that, contrary to recent claims, only F(R) ∝ R^{3/2} satisfies Noether symmetry conditions without gauge, clarifying misconceptions in the field.

Findings

Only F(R) ∝ R^{3/2} satisfies Noether symmetry equations.

Setting gauge to zero restricts solutions to n=2, which does not satisfy field equations.

Non-zero gauge does not yield new admissible forms of F(R).

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.