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

TL;DR

This paper explores classical and quantum cosmological models within Hořava-Lifshitz gravity, deriving solutions for different universe geometries and analyzing quantum effects that could prevent singularities.

Contribution

It provides exact classical solutions and quantizes the model using Wheeler-DeWitt approach, highlighting corrections from Hořava-Lifshitz gravity and their implications.

Findings

Exact classical solutions for flat, closed, and open universes.

Quantum wave functions suggesting possible singularity avoidance.

Discussion of corrections from Hořava-Lifshitz gravity compared to Einstein-Hilbert.

Abstract

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 ADM representation of the action corresponding to this model, we construct the Lagrangian in terms of the minisuperspace variables and show that in comparison with the usual Einstein-Hilbert gravity, there are some correction terms coming from the Ho\v{r}ava theory. Either in the matter free or in the case when the considered universe is filled with a perfect fluid, the exact solutions to the classical field equations are obtained for the flat, closed and open FRW model and some discussions about their possible singularities are presented. We then deal with the quantization of the model in the context of the Wheeler-DeWitt approach of quantum cosmology to find the cosmological wave function. We use the resulting wave functions to investigate the possibility of the avoidance of classical singularities due to quantum effects.