Ho\v{r}ava-Lifshitz Quantum Cosmology

TL;DR

This paper explores quantum cosmology within the Hořava-Lifshitz gravity framework, deriving the Wheeler-deWitt equation, analyzing solutions, and demonstrating how classical universe behavior emerges from quantum states, especially with a positive cosmological constant.

Contribution

It provides a minisuperspace quantum cosmology model for Hořava-Lifshitz gravity without detailed balance, including solutions to the Wheeler-deWitt equation and analysis of quantum-to-classical transition.

Findings

Normalizable wave function for zero cosmological constant

Exponential growth of scale factor with positive cosmological constant

Recovery of general relativity behavior at late times

Abstract

In this work, a minisuperspace model for the projectable Ho\v{r}ava-Lifshitz (HL) gravity without the detailed balance condition is investigated. The Wheeler-deWitt equation is derived and its solutions are studied and discussed for some particular cases where, due to HL gravity, there is a "potential barrier" nearby $a=0$. For a vanishing cosmological constant, it is found a normalizable wave function of the universe. When the cosmological constant is non-vanishing, the WKB method is used to obtain solutions for the wave function of the universe. Using the Hamilton-Jacobi equation, one discusses how the transition from quantum to classical regime occurs and, for the case of a positive cosmological constant, the scale factor is shown to grow exponentially, hence recovering the GR behaviour for the late universe.