DeWitt wave function in Ho\v{r}ava-Lifshitz cosmology with tensor perturbation

TL;DR

This paper constructs a well-behaved DeWitt wave function in Hořava-Lifshitz cosmology with tensor perturbations, overcoming issues present in general relativity by leveraging HL gravity's higher-dimensional operators.

Contribution

It analytically and numerically demonstrates the regularity of the DeWitt wave function with tensor perturbations in HL cosmology, unlike in general relativity.

Findings

DeWitt wave function vanishes at the big-bang singularity.

Tensor perturbations are regular and scale-invariant in HL gravity.

Numerical results confirm the wave function's well-behaved nature near the singularity.

Abstract

We present a well-tempered DeWitt wave function, which vanishes at the classical big-bang singularity, in Ho\v{r}ava-Lifshitz (HL) cosmology with tensor perturbation, both analytically and numerically. In general relativity, the DeWitt wave function is ill-behaved once the tensor perturbation is taken into account. This is essentially because the amplitude of the perturbation diverges at the singularity and the perturbative expansion completely breaks down. On the other hand, in HL gravity it is known that the higher dimensional operators required by the perturbative renormalizability render the tensor perturbation scale-invariant and regular all the way up to the singularity. In this paper we analytically show that in $d+1$ dimensional HL gravity the DeWitt wave function for tensor perturbation is indeed well-defined around the classical big-bang singularity. Also, we numerically demonstrate the well-behaved DeWitt wave function for tensor perturbation from the big-bang to a finite size of the Universe.