Quantum to classical transition in the Ho\v{r}ava-Lifshitz quantum cosmology

TL;DR

This paper investigates the quantum-to-classical transition in Hořava-Lifshitz quantum cosmology using Wigner functions and superpositions, analyzing quantum fluctuations and effects of perturbations like a cosmological constant.

Contribution

It introduces a quasi-Gaussian superposition approach to connect quantum superpositions with classical trajectories in HL cosmology, including effects of perturbations and a cosmological constant.

Findings

Wigner functions describe quantum-classical matching conditions.

Quantum fluctuations quantify nonclassicality in the model.

Cosmological constant influences the universe's age and matter density profile.

Abstract

A quasi-Gaussian quantum superposition of Ho\v{r}ava-Lifshitz (HL) stationary states is built in order to describe the transition of the quantum cosmological problem to the related classical dynamics. The obtained HL phase-space superposed Wigner function and its associated Wigner currents describe the conditions for the matching between classical and quantum phase-space trajectories. The matching quantum superposition parameter is associated to the total energy of the classical trajectory which, at the same time, drives the engendered Wigner function to the classical stationary regime. Through the analysis of the Wigner flows, the quantum fluctuations that distort the classical regime can be quantified as a measure of (non)classicality. Finally, the modifications to the Wigner currents due to the inclusion of perturbative potentials are computed in the HL quantum cosmological context. In particular, the inclusion of a cosmological constant provides complementary information that allows for connecting the age of the Universe with the overall stiff matter density profile.