Evolution of Dynamical Coupling in Scalar Tensor Theory from Noether Symmetry

We present the gravitational coupling function $\omega(\phi)$ in the vacuum scalar-tensor theory as allowed by the Noether symmetry. We also obtain some exact cosmological solutions in the spatially homogeneous and isotropic background thereby showing that the attractor mechanism is not effective enough to reduce the theory to Einstein theory. It is observed that, asymptotically, the scalar tensor theory goes over to Einstein theory with finite value of $\omega$. This work thus supports earlier works in this direction.