Appearance of a classical mixmaster universe from the no-boundary quantum state

Abstract

We investigate the appearance of the classical anisotropic universe from the no-boundary quantum state according to the prescription proposed by Hartle, Hawking, and Hertog. Our model is homogeneous, anisotropic, closed universes with a minimally coupled scalar field and cosmological constant. We found that there are an ensemble of classical Lorentzian histories with anisotropies and experience inflationary expansion at late time, and the probability of histories with anisotropies are lower than isotropic histories. Thus, the no-boundary condition may be able to explain the emergence of our Universe. If the classical late time histories are extended back, some become singular by the existence of initial anisotropies with large accelerations. However, we do not find any chaotic behavior of anisotropies near the initial singularity.