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

Recently, some authors have made a falsifiable claim that Noether gauge symmetry for F® theory of gravity coupled to a tachyon field enforces gauge to vanish and leads to F® \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® theory of gravity in vacuum or in matter dominated era admits trivial Noether symmetry for F® \propto R^{3/2}, because z = a^2, a being the scale factor, becomes cyclic for F® \propto R^{3/2}. Further, it has already been noticed that F® 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® 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® gravity. Since, canonization of a general F® theory of gravity is only possible treating R as the auxiliary variable, so we conclude that in general Noether symmetry of F® theory of gravity is obscure.