Chaplygin Gas Ho\v{r}ava-Lifshitz Quantum Cosmology

TL;DR

This paper explores the quantum cosmology of the Chaplygin gas within Hořava-Lifshitz gravity, deriving solutions that suggest a singularity-free universe at the quantum level.

Contribution

It provides exact classical and quantum solutions for the Chaplygin gas Hořava-Lifshitz cosmology using Schutz formalism and constructs wave packets to analyze the universe's evolution.

Findings

Quantum solutions avoid singularities unlike classical ones

Wave packets show non-singular behavior of the scale factor

Expectation value of the scale factor remains finite

Abstract

In this paper, we study the Chaplygin gas Ho\v{r}ava-Lifshitz quantum cosmology. Using Schutz formalism and Arnowitt-Deser-Misner decomposition, we obtain the corresponding Schr\"{o}dinger-Wheeler-DeWitt equation. We obtain exact classical and quantum mechanical solutions and construct wave packets to study the time evolution of the expectation value of the scale factor for two cases. We show that unlike classical solutions and upon choosing appropriate initial conditions, the expectation value of the scale factor never tends to the singular point which exhibits the singularity-free behavior of the solutions in the quantum domain.