Quintessential and phantom power-law solutions in scalar tensor model of dark energy

We consider a scalar-tensor model of dark energy with kinetic and Gauss Bonnet couplings. We study the conditions for the existence of quintessential and phantom power-law expansion, and also analyze these conditions in absence of potential (closely related to string theory). A mechanism to avoid the Big Rip singularity in various asymptotic limits of the model has been studied. It was found that the kinetic and Gauss-Bonnet couplings might prevent the Big Rip singularity in a phantom scenario. The autonomous system for the model has been used to study the stability properties of the power-law solution, and the centre manifold analysis was used to treat zero eigenvalues.