>>13726035He is talking about the Hartle Hawking no boundary proposal. Within canonical gravity with a spacelike slicing of a 3d compact manifold such as global deSitter, (i.e using a naive quantization of Einstein Hilbert action, by imposing the constraints on the Hilbert space leading to the Wheeler deWitt equation) his statement is that the initial state must be continued to Euclidean time and is a compact Euclidean 4-manifold. This statement makes sense and is probably correct.
However this naive quantization of gravity fails for a simple reason, the action is non-renormalizable. What we need is a proper UV completion like string theory, and I am not completely sure whether the higher derivative terms coupled to Einstein Hilbert action actually allow this particular proposal.
