It has been shown earlier that Noether symmetry does not admit a form of ( ) corresponding to an action in which ( ) is coupled to scalar-tensor theory of gravity or even for pure ( ) theory of gravity taking anisotropic model into account. Here, we prove that ( ) theory of gravity does not admit Noether symmetry even if it is coupled to tachyonic field and considering a gauge in addition. To handle such a theory, a general conserved current has been constructed under a condition which decouples higherorder curvature part from the field part. This condition, in principle, solves for the scale-factor independently. Thus, cosmological evolution remains independent of the form of the chosen field, whether it is a scalar or a tachyon.