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

We investigate the Bianchi I cosmology with the homogeneous SU(2) Yang-Mills field governed by the non-Abelian Born-Infeld action. 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 (non-perturbative in $alpha'$) string corrections to the classical EYM action. We give a numerical evidence for the chaos-order transition, and present an analytical proof of regularity of color oscillations in the limit of strong Born-Infeld non-linearity. We also perform some general analysis of the Bianchi I NBI cosmology and derive an exact solution in the case when only the U(1) component of the Yang-Mills field is excited. Our new exact solution generalizes the Rosen solution to the Bianchi I Einstein-Maxwell cosmology to the U(1) Einstein-Born-Infeld theory.