A multidimensional global monopole and nonsingular cosmology

We consider a spherically symmetric global monopole in general relativity in (D=d+2)-dimensional space-time. For γ<d−1, where γ is a parameter characterizing the gravitational field strength, the monopole is shown to be asymptotically flat up to a solid angle defect. In the range d−1< γ<2d(d+1)/(d+2), the monopole space-time contains a cosmological horizon. Outside the horizon, the metric corresponds to a cosmological model of the Kantowski-Sachs type, where spatial sections have the topology ℝ × Sd. In the important case where the horizon is far from the monopole core, the temporal evolution of the Kantowski-Sachs metric is described analytically. The Kantowski-Sachs space-time contains a subspace with a (d+1)-dimensional Friedmann-Robertson-Walker metric, whose possible cosmological application is discussed. Some estimates in the d=3 case show that this class of nonsingular cosmologies can be viable. In particular, the symmetry-breaking potential at late times can give rise to both dark matter and dark energy. Other results, generalizing those known in 4-dimensional space-time, are derived, in particular, the existence of a large class of singular solutions with multiple zeros of the Higgs field magnitude.