The tunneling boundary condition for the wave function of the universe
Abstract
The modern approach to quantum cosmology initiated primarily by Hartle and Hawking and by Vilenkin is described. The results of this approach culminated with the noboundary and the tunneling boundary conditions of the wave function of the Universe. The latter one is emphasized. The tunneling wave function of the Universe is not always similar to a wave function describing usual quantummechanical tunneling. The differences are illustrated using the example of a homogeneous anisotropic minisuperspace model (which is also of interest in its own right). The tunneling wave function of the model is found in the limit of small and large anisotropy. The tunneling wave function is also calculated for an inflationary cosmological model with a variable gravitational constant. The resulting probability distribution for the initial states of the Universe is peaked at the highest maximum of the effective potential V = V_{max}, with the initial value of the Planck mass at approximately V_{max}^{1/4}. The initial states predicted by the tunneling wave functions are exactly the states needed for a long inflation. This is in contrast to the noboundary proposal of Hartle and Hawking which gives a probability distribution which is incompatible with inflationary scenario.
 Publication:

Ph.D. Thesis
 Pub Date:
 1990
 Bibcode:
 1990PhDT.........1D
 Keywords:

 Astronomical Models;
 Boundary Conditions;
 Cosmology;
 Electron Tunneling;
 Probability Distribution Functions;
 Wave Functions;
 Anisotropy;
 Gravitational Constant;
 Quantum Mechanics;
 Astrophysics