# Classical and quantum Chaplygin gas Ho\v{r}ava-Lifshitz scalar-metric cosmology

## TL;DR

This paper explores a cosmological model combining Chaplygin gas and scalar fields within Hořava-Lifshitz gravity, analyzing classical dynamics and quantum wave functions to assess singularity avoidance.

## Contribution

It introduces a novel cosmological model with Chaplygin gas and scalar fields in Hořava-Lifshitz gravity, analyzing both classical and quantum aspects.

## Key findings

- Classical solutions exhibit potential singularities.
- Quantum wave functions suggest possible singularity avoidance.
- Corrections from Hořava-Lifshitz gravity influence dynamics.

## Abstract

In this work, we study the Friedmann-Robertson-Walker cosmology in which a Chaplygin gas is coupled to a non-linear scalar field in the framework of the Ho\v{r}ava-Lifshitz theory. In writing the action of the matter part, we use the Schutz's formalism so that the only degree of freedom of the Chaplygin gas plays the role of an evolutionary parameter. In a minisuperspace perspective, we construct the Lagrangian for this model and show that in comparison with the usual Einstein-Hilbert gravity, there are some correction terms coming from the Ho\v{r}ava theory. In such a set-up and by using of some approximations the classical dynamics of the model is investigated 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.