Inconsistencies of the New No-Boundary Proposal

Understand

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.