Generalization of Instanton-Induced Inflation and Dynamical Compactification

TL;DR

This paper extends the concept of instanton-induced inflation and compactification to more general Einstein manifolds and FLRW metrics, revealing conditions for universe homogeneity and the existence of bouncing solutions in open universes.

Contribution

It generalizes instanton-induced inflation and compactification to broader geometries and explicitly constructs relevant Yang-Mills instantons for these cases.

Findings

Homogeneous and isotropic universe requires a homogeneous internal space.

Explicit Yang-Mills instantons constructed on all considered Einstein manifolds.

Open universe ($k=-1$) admits bouncing solutions, unlike other spatial curvatures.

Abstract

It was shown that Yang-Mills instantons on an internal space can trigger the expansion of our four-dimensional universe as well as the dynamical compactification of the internal space. We generalize the instanton-induced inflation and dynamical compactification to general Einstein manifolds with positive curvature and also to the FLRW metric with spatial curvature. We explicitly construct Yang-Mills instantons on all Einstein manifolds under consideration and find that the homogeneous and isotropic universe is allowed only if the internal space is homogeneous. We then consider the FLRW metric with spatial curvature as a solution of the eight-dimensional Einstein-Yang-Mills theory. We find that open universe $(k=-1)$ admits bouncing solutions unlike the other cases $(k=0, +1)$.