Chaos-order transition in Bianchi type I non-Abelian Born-Infeld cosmology

Abstract

We investigate the Bianchi I cosmology with the homogeneous SU(2) Yang-Mills field governed by the non-Abelian Born-Infeld action. A similar system with the standard Einstein-Yang-Mills (EYM) action is known to exhibit chaotic behavior induced by the Yang-Mills field. When the action is replaced by the Born-Infeld--type non-Abelian action (NBI), the chaos-order transition is observed in the high-energy region. This is interpreted as a smothering effect due to (nonperturbative in ${\ensuremath{\alpha}}^{\ensuremath{'}}$) string corrections to the classical EYM action. We give numerical evidence for the chaos-order transition and present an analytical proof of regularity of color oscillations in the limit of strong Born-Infeld nonlinearity. We also perform a general analysis of the Bianchi I NBI cosmology and derive an exact solution in the case of only the U(1) component excited. Our new exact solution generalizes the Rosen solution of the Bianchi I Einstein-Maxwell cosmology to the U(1) Einstein-Born-Infeld theory.