Hořava-Lifshitz Scalar Field Cosmology: Classical and Quantum Viewpoints

In this paper, we study a projectable Ho\v{r}ava-Lifshitz cosmology without the detailed balance condition minimally coupled to non-linear self-coupling scalar field. minisuperspace framework, super Hamiltonian of presented model is constructed by means which, some classical solutions for scale factor and field are obtained. Since these exhibit various types singularities, came up with quantization in context Wheeler-DeWitt approach quantum cosmology. The resulting wave functions then used investigate possibility avoidance singularities due effects which show themselves important near singularities.