Self-gravitating global monopole and nonsingular cosmology
We consider a global monopole in general relativity, created by a scalar trilet with a global symmetry-breaking potential. Some common features of hedgehog-type solutions with a regular center are established, independent of the choice of the potential. Six types of qualitative behaviour of the solutions are distinguished; we show, in particular, that the metric can contain at most one simple horizon. For the standard Mexican hat potential, the previously known properties of the solutions are confirmed and some new results are obtained. It is shown analytically that solutions with monotonically growing Higgs field and finite energy in the static region exist only in the interval 1 < g < 3, g being the squared energy of spontaneous symmetry breaking in Planck units. The cosmological properties of these globally regular solutions apparently favour 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. Outside the horizon, one obtains a Kantowski-Sachs anisotropic cosmology, which can be made de Sitter at late times by adding a small constant to the potential (by "slightly raising the Mexican hat").
In addition to the monotonic solutions, we present and analyze a sequence of families of new solutions with oscillating Higgs field. These families are parametrized by n, the number of knots of the Higgs field, and exist for g < gn = 6/[(2n+1) (n+2)]; all such solutions possess a horizon and a singularity beyond it.
Most of the results admit D-dimensional extension. In particular, in 5 dimensions, the Kantowski-Sachs space-time outside the horizon contains a a closed 4-dimensional Friedmann-Robertson-Walker subspace. Its expansion starts from a horizon and can be asymptotically linear or de Sitter at large times.