Quantum Creation of a Universe with $\Omega \ne 1$: Singular and Non-Singular Instantons

Abstract

We propose two new classes of instantons which describe the tunneling and/or quantum creation of closed and open universes. The instantons leading to an open universe can be considered as generalizations of the Coleman-De-Luccia solution. They are non-singular, unlike the instantons recently studied by Hawking and Turok, whose prescription has the problem that the singularity is located on the hypersurface connecting to the Lorentzian region, which makes it difficult to remove. We argue that such singularities are harmless if they are located purely in the Euclidean region. We thus obtain new singular instantons leading to a closed universe; unlike the usual regular instantons used for this purpose, they do not require complex initial conditions. The singularity gives a boundary contribution to the action which is small for the instantons leading to sufficient inflation, but changes the sign of the action for small $\varphi$ corresponding to short periods of inflation.

arXiv comment9 pages, revtex, 6 figures, few misprints improved

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• Quantum Creation of an Open Inflationary Universe
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• Instanton Cosmology and Domain Walls from M-theory and String Theory
• Can we have inflation with Omega > 1?
• Probabilities in the landscape: The decay of nearly flat space
• The density parameter and the Anthropic Principle
• The number of negative modes of the oscillating bounces
• Negative Modes of Oscillating Instantons
• Tunneling probability for the birth of an asymptotically DeSitter universe
• Open inflation and the singular boundary
• Open inflation from non-singular instantons: Wrapping the universe with a membrane
• Oscillating instanton solutions in curved space
• Bubbles from Nothing
• Inhomogeneous compact extra dimensions and de Sitter cosmology
• Open inflation from quantum cosmology with a strong nonminimal coupling
• Instantons from Low Energy String Actions
• Open Inflation With Scalar-tensor Gravity
• Singular Instantons Made Regular
• Nonsingular instantons for the creation of open universes
• Positive curvature and scalar field tunneling in the landscape
• Evolution of sub-spaces at high and low energies
• Tunnelling with Bianchi IX Instantons
• Action of Singular Instantons of Hawking-Turok Type