Self-Gravitating Global Monopole and Nonsingular Cosmology

We review some recent results concerning the properties of a spherically symmetric global monopole in (D = d+2)-dimensional general relativity. Some common features of monopole solutions are found independently of the choice of the symmetry-breaking potential. Thus, the solutions show six types of qualitative behavior and can contain at most one simple horizon. For the standard Mexican hat (Higgs) potential, we analytically find the D-dependent range of the parameter γ (characterizing the gravitational field strength) in which there exist globally regular solutions with a monotonically growing Higgs field, containing a horizon and a Kantowski–Sachs (KS) cosmology outside it, with the topology of spatial sections R× S. Their cosmological properties favor the idea that the standard Big Bang might be replaced with a nonsingular static core and a horizon appearing as a result of some symmetry-breaking phase transition on the Planck energy scale. We have also found families of new solutions with an oscillating Higgs field, parametrized by the number of its knots. All such solutions describe space-times of finite size, possessing a regular center, a horizon and a singularity beyond it.