The most probable size of the Universe

It has recently been suggested, by Firouzjahi, Sarangi, and Tye, that string-motivated modifications of the Hartle-Hawking wave function predict that our Universe came into existence from “nothing” with a de Sitter-like spacetime geometry and a spacetime curvature similar to that of “low-scale” models of Inflation. This means, however, that the Universe was quite large at birth. It would be preferable for the initial scale to be close to the string scale (or perhaps the Planck scale). The problem with this, however, is to explain how any initial homogeneity is preserved during the pre-inflationary era, so that inflation can indeed begin. Here we modify a suggestion due to Linde and assume that the Universe was born with the topology of a torus; however, we propose that the size of the torus is to be predicted by the FST wave function. The latter does predict an initial size for the torus at about the string scale, and it also predicts a pre-inflationary spacetime geometry such that chaotic mixing preserves any initial homogeneity until Inflation can begin at a relatively low scale.