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arXiv · 2111.00665

DeWitt boundary condition is consistent in Hořava-Lifshitz quantum gravity

Hiroki Matsui·Shinji Mukohyama·Atsushi Naruko
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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 Hořava-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.

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Hiroki Matsui, Shinji Mukohyama, Atsushi Naruko. 2022-08-05. DeWitt boundary condition is consistent in Hořava-Lifshitz quantum gravity. https://doi.org/10.1016/j.physletb.2022.137340

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