Inconsistencies of the New No-Boundary Proposal

TL;DR

This paper critiques recent proposals for the gravitational path integral in quantum cosmology, demonstrating that they lead to mathematical inconsistencies and physical issues, such as uncontrolled fluctuations and breakdown of perturbation theory.

Contribution

The paper analyzes and refutes recent complex contour proposals for the gravitational path integral, highlighting their mathematical and physical inconsistencies.

Findings

Complex contour integration proposals are inconsistent with well-defined quantum gravity.

The new proposals lead to uncontrolled fluctuations in the path integral.

Vilenkin and Yamada's modification causes perturbation theory breakdown.

Abstract

In previous works, we have demonstrated that the path integral for {\it real, Lorentzian} four-geometries in Einstein gravity yields sensible results in well-understood physical situations, but leads to uncontrolled fluctuations when the "no boundary" condition proposed by Hartle and Hawking is imposed. In order to circumvent our result, new definitions for the gravitational path integral have been sought, involving specific choices for a class of {\it complex} four-geometries to be included. In their latest proposal, Diaz Dorronsoro {\it et al.}~\cite{DiazDorronsoro:2018wro} advocate integrating the lapse over a complex circular contour enclosing the origin. In this note we show that, like their earlier proposal, this leads to mathematical and physical inconsistencies and thus cannot be regarded as a basis for quantum cosmology. We also comment on Vilenkin and Yamada's recent modification of the "tunneling" proposal, made in order to avoid the same problems. We show that it leads to the breakdown of perturbation theory in a strong coupling regime.