Cosmological Analogues of the Bartnik--McKinnon Solutions

Abstract

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, $Λ< \Llow(n)$, 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 $Λ_{\rm reg}(n) > Λ_{\rm crit}(n)$, the solutions are topologically $3$--spheres, the ground state $(n=1)$ being the Einstein Universe. In the intermediate region, that is for $\Llow(n) < Λ< \Lhig(n)$, there exists a discrete family of global solutions with horizon and ``finite size''.