Ho\v{r}ava-Lifshitz scalar field cosmology: classical and quantum viewpoints

TL;DR

This paper explores a Hořava-Lifshitz cosmological model with a scalar field, analyzing classical solutions with singularities and investigating quantum effects that could potentially avoid these singularities.

Contribution

It introduces a quantum cosmology analysis of a Hořava-Lifshitz scalar field model without detailed balance, highlighting the potential for quantum effects to resolve classical singularities.

Findings

Classical solutions exhibit various singularities.

Quantum wave functions suggest possible singularity avoidance.

Quantum effects become significant near classical singularities.

Abstract

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