Unstable no-boundary fluctuations from sums over regular metrics

TL;DR

This paper investigates whether restricting the path integral to regular geometries affects the instability of fluctuations in the no-boundary proposal, finding that the instability persists even without singular off-shell geometries.

Contribution

The study extends previous calculations by considering only regular geometries in the no-boundary path integral, confirming that fluctuations remain unstable.

Findings

Fluctuations are unstable even with regular geometries

Singular off-shell geometries are not the cause of instability

Supports the need for alternative initial condition theories

Abstract

It was recently shown by Feldbrugge et al. that the no-boundary proposal, defined via a Lorentzian path integral and in minisuperspace, leads to unstable fluctuations, in disagreement with early universe observations. In these calculations many off-shell geometries summed over in the path integral in fact contain singularities, and the question arose whether the instability might ultimately be caused by these off-shell singularities. We address this question here by considering a sum over purely regular geometries, by extending a calculation pioneered by Halliwell and Louko. We confirm that the fluctuations are unstable, even in this restricted context which, arguably, is closer in spirit to the original proposal of Hartle and Hawking. Elucidating the reasons for the instability of the no-boundary proposal will hopefully show how to overcome these difficulties, or pave the way to new theories of initial conditions for the universe.