Revisiting Noether symmetry approach in F(R)-tachyon Model

Recently, some authors have made a falsifiable claim that Noether gauge symmetry for F(R) theory of gravity coupled to a tachyon field enforces gauge to vanish and leads to F(R) \propto R^2, with a tachyon potential V(\phi) \propto \phi^{-4}. Here, we show that the analysis is completely wrong since the conserved current does not satisfy the field equations. Earlier, it has been shown that F(R) theory of gravity in vacuum or in matter dominated era admits trivial Noether symmetry for F(R) \propto R^{3/2}, because z = a^2, a being the scale factor, becomes cyclic for F(R) \propto R^{3/2}. Further, it has already been noticed that F(R) does not admit Noether symmetry when coupled to a scalar sector, minimally or non-minimally. Finally, here we show that Noether symmetry is obscure even when F(R) is coupled to a tachyon field. However, Noether symmetry for R^2 gravity coupled to a scalar taking an auxiliary variable Q different from R exists in the literature and it is not recovered from F(R) gravity. Since, canonization of a general F(R) theory of gravity is only possible treating R as the auxiliary variable, so we conclude that in general Noether symmetry of F(R) theory of gravity is obscure.