Mathematics – Logic
Scientific paper
Oct 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999phdt.........6c&link_type=abstract
Thesis (PhD). TUFTS UNIVERSITY, Source DAI-B 60/04, p. 1648, Oct 1999, 122 pages.
Mathematics
Logic
Monopoles
Scientific paper
Topological defects are cosmological objects which can form during phase transitions in the early universe. They have attracted much attention because of their peculiar physical properties, spacetime geometries and cosmological implications. In this thesis, I investigate the properties of topological defects particularly in relation to inflation. The core of defects can inflate if the symmetry-breaking scale is on the order of the Planck mass. When this condition is reached, the size of defects becomes comparable to the horizon scale and the gravitational effect is substantial in the core region. As a consequence of the inflationary behavior at the core, the physical properties of defects can be much different from those of the static case. To begin with, the evolution of a global monopole with an inflating core is investigated. A time-dependent exterior metric is obtained by analytic continuation of a static metric. This is verified by numerically solving the field equations. The metric describes a nonstationary spacetime with a highly anisotropic expansion. The overall spacetime is studied both in vacuum and in a radiation background. It is well known that the gauge monopole becomes a black hole if the symmetry-breaking scale is sufficiently large. At the same time, the core of the monopole begins to inflate. We can, therefore, consider generation of a child-universe inside the monopole which is connected to the exterior by a wormhole structure. Cosmic strings are studied in the context of topological inflation. The core of strings undergoes inflation in both radial and axial directions. The overall picture of string inflation is similar to that of monopoles. Static solutions of cosmic global strings and supermassive gauge strings exhibit a curvature singularity at a finite distance from the center. However, in the course of string evolution with a general time-dependent metric, we observe that no singularity develops in the string geometry. A thin wall approximation is exploited to investigate the dynamics of global monopoles. The core is modeled by de Sitter space, its boundary by a thin wall with a constant energy density, and its exterior by the asymptotic Schwarzschild solution with negative gravitational mass and solid angle deficit. The wall motion determines the monopole dynamics. If the symmetry-breaking scale η is not too large, there exist stable monopole solutions with a well-defined negative mass. If η is large enough, there exist only inflating solutions. For the intermediate η, stable solutions co-exist with inflating ones. However, these solutions appear to be metastable towards inflation. At the end of the work, I introduce a new model of topological defects, so-called vacuumless defects. Such defects can arise in a symmetry-breaking phase transition where the scalar field potential has no minima and is a monotonically decreasing function. The properties of vacuumless defects are quite different from those of the usual defects. The defects in this model are very diffuse objects and the cosmological evolution is distinguishable from the usual defects. Vacuumless defects can also serve as seeds for structure formation, or produce an appreciable density of mini-black holes. The gravitational field of vacuumless strings and monopoles is also discussed.
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