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.
