Classical and quantum Ho\v{r}ava-Lifshitz cosmology in a minisuperspace perspective

摘要

We study the classical and quantum models of a Friedmann-Robertson-Walker(FRW) cosmology in the framework of the gravity theory proposed by Ho\v{r}ava,the so-called Ho\v{r}ava-Lifshitz theory of gravity. Beginning with the ADMrepresentation of the action corresponding to this model, we construct theLagrangian in terms of the minisuperspace variables and show that in comparisonwith the usual Einstein-Hilbert gravity, there are some correction terms comingfrom the Ho\v{r}ava theory. Either in the matter free or in the case when theconsidered universe is filled with a perfect fluid, the exact solutions to theclassical field equations are obtained for the flat, closed and open FRW modeland some discussions about their possible singularities are presented. We thendeal with the quantization of the model in the context of the Wheeler-DeWittapproach of quantum cosmology to find the cosmological wave function. We usethe resulting wave functions to investigate the possibility of the avoidance ofclassical singularities due to quantum effects.