Quantum cosmology in Ho\v{r}ava-Lifshitz gravity

Abstract

Quantum cosmology is studied within the framework of the minimal quantum gravity theory proposed by Ho\v{r}ava. For this purpose we choose the Kantowski-Sachs (KS) model and construct the corresponding Wheeler-DeWitt equation. We study the solution to this equation in the ultraviolet limit for different values of the running parameter {\lambda} of the theory. It is observed that the wave packet for this Universe changes completely compared with the one observed in the infrared (general relativity) regime. We also look at the classical solutions by means of a WKB semiclassical approximation. It is observed that if {\lambda} takes its relativistic value {\lambda} = 1 a generalized KS metric is obtained which differs from the usual KS solution in general relativity by an additional term arising from the higher-order curvature terms in the action and which dominates the behavior of the solution for very small values of the time parameter. We discuss the physical properties of this solution by comparing it with the usual KS solution in general relativity. The resulting solution has no horizons but singularities.