Quantum creation of universes

Abstract

A cosmological wave function describing the tunneling of the Universe from "nothing" into a de Sitter space is found in a simple minisuperspace model. The tunneling probability is proportional to $\mathrm{exp}(\frac{\ensuremath{-}3}{8{G}^{2}{\ensuremath{\rho}}_{v}})$, where ${\ensuremath{\rho}}_{v}$ is the vacuum energy density at an extremum of the effective potential $V(\ensuremath{\varphi})$. The tunneling is most probable to the highest maximum of $V(\ensuremath{\varphi})$.