Multidimensional Global Monopole and Nonsingular Cosmology

Abstract

We consider a spherically symmetric global monopole in general relativity in $(D=d+2)$-dimensional spacetime. The monopole is shown to be asymptotically flat up to a solid angle defect in case $\gamma < d-1$, where $\gamma$ is a parameter characterizing the gravitational field strength. In the range $d-1< \gamma < 2d(d+1)/(d+2)$ the monopole space-time contains a cosmological horizon. Outside the horizon the metric corresponds to a cosmological model of Kantowski-Sachs type, where spatial sections have the topology ${\R\times \S}^d$. In the important case when 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, and its possible cosmological application is discussed. Some numerical estimations in case $d=3$ are made showing that this class of nonsingular cosmologies can be viable. Other results, generalizing those known in the 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.