Quantum Creation of a Universe with $\Omega \not = 1$: Singular and Non-Singular Instantons

TL;DR

This paper introduces new classes of instantons for quantum universe creation, including non-singular and singular types, which generalize existing solutions and address issues with previous models.

Contribution

It presents novel instanton solutions for universe creation that are either non-singular or singular but well-behaved, expanding the theoretical framework beyond prior models.

Findings

Non-singular instantons generalize Coleman-De-Luccia solutions.

Singular instantons are shown to be harmless if singularities are in Euclidean regions.

Instantons can lead to sufficient inflation without complex initial conditions.

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 $\phi$ corresponding to short periods of inflation.