Isotropization by scalar field driven inflation and the cosmological quantum boundary

Publisher Website
Google Scholar
Abstract
We derive the Wheeler‐de Witt equation for the scalar field of mass m > 0 in a Bianchi‐type I universe. We argue that classical trajectories become possible at h2 ⩽ αtp‐2, h being the mean Hubble value and tp the Planck time. We feel justified to set the numerical constant α ≈︁ 1. We discuss this condition in geometrically invariant quantities and compare it with ⩽tp‐4. The proposed quantum boundary of classical trajectories represents a 3‐dimensional sphere in the 4‐space of the dynamical system. Equipartition of the initial energy over field (m < mp) and shear variables at the quantum boundary will cause inflation with a probability p of the order p = 1 ‐ m/mp thus, p = 1 ‐ 10‐4 for m taken from GUT. In the course of the inflationary stage the initially arbitrarily large shear‐anisotropy exponentially decays.