Hartle-Hawking sum over all possible metrics?

[Suekdccia]

TL;DR Summary

According to Hartle-Hawking state, could we build a sum over all possible metrics (including non-compact ones)?

Physicists Stephen W Hawking and James B Hartle 1 proposed that the universe, in its origins, had no boundary conditions both in space and time.

To do that, they proposed a sum over all compact euclidean compact metrics. I have heard that they only considered these metrics in order to simplify the calculations (since their aim was to prove that our universe was the most likely outcome). Then, does that mean that they originally considered a sum over all possible metrics (not only compact euclidean ones)? Did they really considered the subset of compact Euclidean metrics just to simplify the calculations of the model (but their model was actually considering the sum over all possible metrics)?

 

[azntoon]

Yes, Hawking and Hartle considered a sum over all possible metrics in order to prove that our universe was the most likely outcome. However, in order to simplify the calculations, they focused on a subset of compact Euclidean metrics. This allowed them to calculate the probability of a given universe much more easily. Thus, their model does consider the sum over all possible metrics, but the focus on the subset of compact Euclidean metrics allowed them to simplify the calculations.