Posted: Jan 13, 2018 10:56 am
The discussions of the mathematics went on for years before the Steinhardt-Turok et al works and Turok's later simplification. Here's a note on the geometry of Hawking-Turok's instanton that concludes:
Rotating the Wick around the original coordinate...
In summary, what the solution of Hawking and Turok requires to lead to an open universe in a natural way is, on the one hand, the complexification from the real to the Euclidean metric and, on the other hand, an extension into the open universe sector which should be accompanied by a rotation of the scale factor induced only by the Wick rotation of the original σ coordinate.
Rotating the Wick around the original coordinate...