cosmology - Why is Hawking's No Boundary condition described in terms of an instanton if there's no tunneling?

Regarding his take about combining No Boundary proposal with inflation theory (Hawking and Turok), he talks about the "pea instanton".

To my very limited understanding I thought instantons were only for describing quantum tunneling phenomena. The No Boundary proposal doesn't subscribe to this, it just says that the Euclideanized 4-spatial-dimensioned pre-Planck-era universe was always there and there was no t=0?

Or does it actually involve a tunneling process like Vilenkin's?

Answer

Analogously to the use of SU(2) instantons for describing tunelling between topologically distinct vacuum sectors, I've heard people talk about gravitational instantons as describing a tunneling process connecting "nothing" with an expanding Minkowski signature universe. People talk heuristically of a universe having emerged by tunnelling from "nothing".

When it comes to cosmology, one must be cautious with the word “tunneling” since it now refers to the “birth of a cosmos from nothing”. What’s more, the relevant path-integral now involves a sum over 4-geometries, which seems much farther from mathematical (or even physical) respectability than what we were considering earlier. Still, if we are willing to neglect a number of important complications, we can make the problem seem remarkably close to more homely examples of tunneling, like the one treated above. This of course, is basically the view people have taken in discussing “creation of the universe via a gravitational instanton”.