Classical and quantum cosmology of K-essentially modified R² and pure R^p gravity

We present a gravitational action with a modified higher order term of a combination of scalar curvature and Lagrangian density of a scalar field. This type of models has been considered first by Cruz-Dombriz et al. The classical and quantum cosmologies governed by the modified action are studied. Models described by a positive-definite action and a pure arbitrary-powered scalar curvature action without the standard Einstein-Hilbert term are also investigated. We show some particular cases in which exact solutions can be obtained.