DeWitt boundary condition is consistent in Ho\v{r}ava-Lifshitz quantum gravity

TL;DR

This paper examines the DeWitt boundary condition in quantum cosmology, demonstrating its consistency within Hořava-Lifshitz gravity and providing explicit solutions for the wave function of the universe with perturbations.

Contribution

It shows that Hořava-Lifshitz gravity yields a consistent DeWitt wave function, unlike general relativity, and provides exact and systematic solutions near the big-bang singularity.

Findings

DeWitt wave function not suppressed by perturbations in general relativity

Exact analytic DeWitt wave function in z=3 Hořava-Lifshitz gravity

Systematic expansion of wave function around singularity with perturbations

Abstract

In quantum cosmology the DeWitt boundary condition is a proposal to set the wave function of the universe to vanish at the classical big-bang singularity. In this Letter, we show that in many gravitational theories including general relativity, the DeWitt wave function does not take a desired form once tensor perturbations around a homogeneous and isotropic closed universe are taken into account: anisotropies and inhomogeneities due to the perturbations are not suppressed near the classical singularity. We then show that Ho\v{r}ava-Lifshitz gravity provides a satisfactory DeWitt wave function. In particular, in the limit of $z=3$ anisotropic scaling, we find an exact analytic expression for the DeWitt wave function of the universe with scale-invariant perturbations. In general cases with relevant deformations, we show that the DeWitt wave function can be systematically expanded around the classical big-bang singularity with perturbations under control.