Evolution of dynamical coupling in scalar tensor theory from Noether symmetry

We present the gravitational coupling function omega(phi) in the vacuum sca lar-tensor theory as allowed by the Noether symmetry. We also obtain some e xact cosmological solutions in the spatially homogeneous and isotropic back ground thereby showing that the attractor mechanism is not effective enough to reduce the theory to Einstein theory. It is observed that, asymptotical ly, the scalar tensor theory goes over to Einstein theory with a finite val ue of omega. This work thus supports earlier works in this direction.