Damped perturbations in the no-boundary state

TL;DR

This paper calculates the no-boundary path integral exactly in a Bianchi IX model, showing that large perturbations are damped, supporting the original no-boundary proposal with a consistent vacuum state.

Contribution

It provides an exact evaluation of the no-boundary path integral in a Bianchi IX minisuperspace, including non-linear backreaction effects.

Findings

Large perturbations are strongly damped.

The predictions align with the original semiclassical no-boundary proposal.

The model implements the no-boundary condition with a zero initial scale factor.

Abstract

We evaluate the no-boundary path integral exactly in a Bianchi IX minisuperspace with two scale factors. In this model the no-boundary proposal can be implemented by requiring one scale factor to be zero initially together with a judiciously chosen regularity condition on the momentum conjugate to the second scale factor. Taking into account the non-linear backreaction of the perturbations we recover the predictions of the original semiclassical no-boundary proposal. In particular we find that large perturbations are strongly damped, consistent with vacuum state wave functions.