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)∝R n (where n≠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 \(F(R) \propto R^{\frac{3}{2}}\) 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 form that Noether symmetry admits is \(F(R) \propto R^{\frac{3}{2}}\). Noether symmetry with non-zero gauge has also been studied explicitly here, to show that it does not produce anything new.
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Sk, N., Sanyal, A.K. Revisiting Noether gauge symmetry for F(R) theory of gravity. Astrophys Space Sci 342, 549–555 (2012). https://doi.org/10.1007/s10509-012-1184-5
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DOI: https://doi.org/10.1007/s10509-012-1184-5