Yang-Mills Cosmologies and Collapsing Gravitational Sphalerons

TL;DR

This paper explores cosmological solutions involving oscillating Yang-Mills fields that transition between vacua, modeling collapsing gravitational sphalerons and analyzing fermion production and energy level crossing, with extensions to include axion fields.

Contribution

It introduces new cosmological solutions with Yang-Mills fields passing between vacua, modeling gravitational sphalerons and analyzing fermion behavior in these backgrounds.

Findings

Fermion energy levels cross from negative to positive during gauge field evolution.

Explicit analysis of Dirac equation in Yang-Mills cosmological backgrounds.

Generalization of solutions to include axion fields.

Abstract

Cosmological solutions with a homogeneous Yang-Mills field which oscillates and passes between topologically distinct vacua are discussed. These solutions are used to model the collapsing Bartnik-McKinnon gravitational sphaleron and the associated anomalous production of fermions. The Dirac equation is analyzed in these backgrounds. It is shown explicitly that a fermion energy level crosses from the negative to positive energy spectrum as the gauge field evolves between the topologically distinct vacua. The cosmological solutions are also generalized to include an axion field.