Quantum Cosmology

An elementary review of quantum cosmology. (Talk given at Texas/Pascos 1992 at Berkeley)Comment: 10 pages, TUTP-92-1

The No-Boundary Wave Function and the Duration of the Inflationary Period

For the simplest minisuperspace model based on a homogeneous, isotropic metric and a minimally coupled scalar field we derive analytic expressions for the caustic which separates Euklidean and Minkowskian region and its breakdown value \p_*. This value represents the prediction of the no-boundary wave function for the scalar field at the beginning of inflation. We use our results to search for inflationary models which can render the no-boundary wave function consistent with the requirement of a sufficiently long inflationary period.Comment: 11 pages, TUM-HEP-206/94, 2 figures (added as uu-encoded postscript file

The wave function discord

Linde's proposal of a Euclidean path integral with the ``wrong'' sign of Euclidean action is often identified with the tunneling proposal for the wave function of the universe. However, the two proposals are in fact quite different. I illustrate the difference and point out that recent criticism by Hawking and Turok does not apply to the tunneling proposal.Comment: 7 pages, 2 figure

Quantum Cosmology of Classically Constrained Gravity

In hep-th/0506040 we discussed a classically constrained model of gravity. This theory contains known solutions of General Relativity (GR), and admits solutions that are absent in GR. Here we study cosmological implications of some of these new solutions. We show that a spatially-flat de Sitter universe can be created from ``nothing''. This universe has boundaries, and its total energy equals to zero. Although the probability to create such a universe is exponentially suppressed, it favors initial conditions suitable for inflation. Then we discuss a finite-energy solution with a nonzero cosmological constant and zero space-time curvature. There is no tunneling suppression to fluctuate into this state. We show that for a positive cosmological constant this state is unstable -- it can rapidly transition to a de Sitter universe providing a new unsuppressed channel for inflation. For a negative cosmological constant the space-time flat solutions is stable.Comment: 17 pages; 6 figure

Fine Structure Constant in the Spacetime of a Cosmic String

We calculate the fine structure constant in the spacetime of a cosmic string. In the presence of a cosmic string the value of the fine structure constant reduces. We also discuss on numerical results.Comment: 5 pages, Published in Phys. Lett.

The quantum cosmology debate

I review the tunneling, Hartle-Hawking and Linde proposals for the wave function of the universe and comment on the recent work on quantum creation of open universes.Comment: Contribution to the debate on quantum cosmology at the COSMO-98 meeting. 9 pages, 6 figure