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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 unstable 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 et
al. (arXiv:1804.01102) 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.