Cosmological analogues of the Bartnik-McKinnon solutions.

We present a numerical classification of the spherically symmetric, static solutions to the Einstein–Yang–Mills equations with cosmological constant Λ. We find three qualitatively different classes of configurations, where the solutions in each class are characterized by the value of Λ and the number of nodes, n, of the Yang–Mills amplitude. For sufficiently small, positive values of the cosmological constant, Λ < Λcrit(n), the solutions generalize the Bartnik–McKinnon solitons, which are now surrounded by a cosmological horizon and approach the deSitter geometry in the asymptotic region. For a discrete set of values Λreg(n) > Λcrit(n), the solutions are topologically 3–spheres, the ground state (n = 1) being the Einstein Universe. In the intermediate region, that is for Λcrit(n) < Λ < Λreg(n), there exists a discrete family of global solutions with horizon and “finite size”. On leave of absence from Tbilisi Mathematical Institute, 380093 Tbilisi, Georgia