Quantum Singularities in Horava-Lifshitz Cosmology

TL;DR

This paper investigates the quantum behavior of a universe described by Horava-Lifshitz gravity, showing it remains nonsingular at the quantum level through expectation values and initial conditions, thus addressing classical singularities.

Contribution

It demonstrates quantum nonsingularity in HL cosmology using standard quantum cosmology techniques, with and without the detailed balance condition.

Findings

The expectation value of the scale factor never vanishes.

Quantum dynamics are uniquely determined without boundary conditions when abandoning detailed balance.

The universe remains nonsingular at the quantum level.

Abstract

The recently proposed Horava-Lifshitz (HL) theory of gravity is analyzed from the quantum cosmology point of view. By employing usual quantum cosmology techniques, we study the quantum Friedmann-Lemaitre-Robertson-Walker (FLRW) universe filled with radiation in the context of HL gravity. We find that this universe is quantum mechanically nonsingular in two different ways: the expectation value of the scale factor $<a>(t)$ never vanishes and, if we abandon the detailed balance condition suggested by Horava, the quantum dynamics of the universe is uniquely determined by the initial wave packet and no boundary condition at $a=0$ is indeed necessary.