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In this work were studied quantum models of a Friedmann-Robertson-Walker(FRW) cosmology in the framework of the gravity's theory proposed byHo\v{r}ava, the so-called Ho\v{r}ava-Lifshitz theory of the gravity. It wasused the Ho\v{r}ava theory for the projectable Ho\v{r}ava-Lifshitz (HL) gravitywithout the detailed balance condition. Following the quantization of the modelin the context of Wheeler-DeWitt approach and taking in account the orderingfactor for operators were found the cosmological wave function. Solutions werestudied and the results were discussed for some particular cases close ofinitial singularity. The resulting wave functions were used to investigate thepossibility of to avoid the classical singularities due to quantum effects andfor analyzing the entanglement entropy. In the ultraviolet phase were found theexistence of cosmological wave function with a relation between the orderingfactor and coupling constants showing their quantum nature, then it waspossible to provide an explicit evolution of the cosmological entanglemententropy in this stage. The interpretation of Bohm-De Broglie was used todiscussion of the solutions.

Quantum Ho\v{r}ava-Lifshitz cosmology and the quantum nature of coupling corrections of HL gravity