Noether symmetry in the higher order gravity theory

Noether symmetry for scalar tensor theory including curvature quadratic term has been explored, with the introduction of an auxiliary variable. Introduction of an auxiliary variable in the action facilitates in transforming the fourth order field equations to the second order field equations. Introduction of Noether symmetry in the action yield the coupling function ω(φ) and the potential V(φ). The application of Noether symmetry further turned out to be powerful tool to find the solution of the field equations. A few physically reasonable solutions like power law inflation are presented.