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 higher-order 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. 1. Introduction Interest in theory of gravity has increased predominantly in recent years, since it appears to explain most of the presently available cosmological data unifying early inflation with late time cosmic acceleration (see [1, 2] for recent reviews and also references therein). However, most of these interesting results are the outcome of scalar-tensor equivalence under some arbitrary choice of the form of . It is, therefore, important to test if the same results are obtainable from theory of gravity without invoking scalar-tensor equivalence. But then how to choose a form of out of indefinitely large number of curvature invariant terms and how to find exact solutions are big questions. From physical ground, namely, to obtain a renormalizable theory of gravity, a form of had been found in the context of early universe, which contains ghosts [3]. A ghost-free action has also been presented in recent years [4, 5]. Likewise, the only physically meaningful technique to obtain a form of to explain late time cosmological evolution is to invoke Noether symmetry as a selection rule. This requires canonical formulation, and for a general theory of gravity, it is only possible treating as an auxiliary variable, provided (here, prime represents derivative with respect to ). In the process, it is possible to construct a point Lagrangian, and one can demand Noether symmetry to find a suitable form of . Following this technique, several authors [6–12] have found in the Robertson-Walker metric both in vacuum and pressureless dust . Although such a form of shows accelerating expansion in the matter dominated era ( ), nevertheless, early decelerating phase tracks as in the matter dominated era instead of usual and in the radiation dominated era ( ) instead of usual , creating problem in explaining structure formation [13]. Thus, alone, in the
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