Gravitational instantons and internal dimensions

TL;DR

This paper investigates instanton solutions in general relativity with scalar fields, focusing on metrics with extra compact dimensions, and compares their action to higher-dimensional Hawking-Turok instantons to assess their likelihood as initial universe conditions.

Contribution

It introduces a class of product metric instantons with extra dimensions and compares their action to Hawking-Turok instantons, revealing the latter generally have lower action.

Findings

Product metric instantons have local minima in action.

Hawking-Turok instantons have lower action than product metric instantons.

Extra compact dimensions do not favor initial conditions due to higher action.

Abstract

We Study instanton solutions in general relativity with a scalar field. The metric ansatz we use is composed of a particular warp product of general Einstein metrics, such as those found in a number of cosmological settings, including string cosmology, supergravity compactifications and general Kaluza Klein reductions. Using the Hartle-Hawking prescription the instantons we obtain determine whether metrics involving extra compact dimensions of this type are favoured as initial conditions for the universe. Specifically, we find that these product metric instantons, viewed as constrained instantons, do have a local minima in the action. These minima are then compared with the higher dimensional version of the Hawking-Turok instantons, and we argue that the latter always have lower action than those associated with these product metrics.