James B. Hartle. S. W. Hawking, Thomas Hertog
The evolution of the universe is determined by its quantum state. The wave function of the universe obeys the constraints of general relativity and in particular the Wheeler-DeWitt equation. For non-zero \Lambda, we show that the complexified solutions of the Wheeler-DeWitt equation at large volume have two regions in which geometries are asymptotically real. In one the histories are Euclidean asymptotically anti-de Sitter, in the other they are Lorentzian asymptotically de Sitter. We illustrate this by an explicit calculation in a homogeneous isotropic minisuperspace model with negative \Lambda, and a scalar moving in a negative potential. It is shown that the wave function in this theory can predict an ensemble of inflationary universes that asymptote to de Sitter space.
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http://arxiv.org/abs/1207.6653
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