Topological Inflation, without the Topology

Abstract

We extend the `topological inflation' of Linde and Vilenkin to {\em unstable} monopoles. This allows the monopole to decay; not inflating eternally, as topological inflation demands. Such a situation happens naturally in some Grand Unified Theories --- such as supersymmetric flipped-$SU(5)$. We analyse analytically the dynamics of inflating monopoles to determine the equations governing the expansion, additionally recovering the bound on the scale of symmetry breaking found numerically by Sakai {\em et. al.} The latter half of this paper is devoted to the Cosmology of inflating unstable monopoles --- which is an example of an inhomogeneous cosmology. We describe how such a monopole may be formed and how long it inflates for --- finding it to be a random process. We then derive how cosmological parameters, such as density and temperature, are distributed at the end of inflation, and how the Universe reheats as the monopole decays. The general conclusion of this work is that such inflation creates a local region of relatively flat, homogenous and isotropic Universe surrounded by pre-GUT matter.