Chapter 3
Topological defects
3.1 Introduction
When a phase transition occurs in the early universe, the alignment of the
spontaneous symmetry breaking expectation value may be different in adjacent
causal domains. In that case, topologically stable objects such as domain walls,
cosmic strings and magnetic monopoles, referred to as 'topological defects',
can be formed [I J. Similar topological defects are familiar in condensed state
physics. For example, a ferromagnet is, in general, divided into domains
where the spontaneous magnetization is aligned in a definite direction. At the
boundary between two such domains, the direction of the magnetization evolves
continuously between its direction in one domain and its direction in the adjacent
domain to form a so-called 'domain wall'. Another example of a topological
defect is provided by a magnetic flux line in a type II superconductor. In this case,
the phase of a complex scalar field (associated with the Cooper-paired electron
condensate) changes by 211'n, where n is an integer, in going around a closed
loop surrounding the flux line and the flux line carries n units of a quantum
of magnetic flux. In addition to these two-dimensional and one-dimensional
topological defects, there are also point defects. These are most familiar in
a particle physics context as magnetic monopole solutions though analogous
objects occur in superftuid 3He. In the context of particle physics and early
cosmology, the corresponding topological defects are associated with the vacuum
expectation values (VEVs) in electroweak or grand unified theories or with the
various moduli that occur in superstring theories.
Once such topological defects have been formed at a phase transition in
the early universe, they can manifest themselves in various ways. The simplest
manifestations are as a potentially substantial contribution to the energy density
of the universe or, in the case of magnetic monopoles, as a relic density of
particles carrying magnetic charge. More subtle manifestations are also possible.
For example, relic cosmic strings may act as gravitational lenses or produce
temperature fluctuations in the cosmic microwave background radiation.
DOl: 10.1201/9780367806637-3
65
Topological defects
3.1 Introduction
When a phase transition occurs in the early universe, the alignment of the
spontaneous symmetry breaking expectation value may be different in adjacent
causal domains. In that case, topologically stable objects such as domain walls,
cosmic strings and magnetic monopoles, referred to as 'topological defects',
can be formed [I J. Similar topological defects are familiar in condensed state
physics. For example, a ferromagnet is, in general, divided into domains
where the spontaneous magnetization is aligned in a definite direction. At the
boundary between two such domains, the direction of the magnetization evolves
continuously between its direction in one domain and its direction in the adjacent
domain to form a so-called 'domain wall'. Another example of a topological
defect is provided by a magnetic flux line in a type II superconductor. In this case,
the phase of a complex scalar field (associated with the Cooper-paired electron
condensate) changes by 211'n, where n is an integer, in going around a closed
loop surrounding the flux line and the flux line carries n units of a quantum
of magnetic flux. In addition to these two-dimensional and one-dimensional
topological defects, there are also point defects. These are most familiar in
a particle physics context as magnetic monopole solutions though analogous
objects occur in superftuid 3He. In the context of particle physics and early
cosmology, the corresponding topological defects are associated with the vacuum
expectation values (VEVs) in electroweak or grand unified theories or with the
various moduli that occur in superstring theories.
Once such topological defects have been formed at a phase transition in
the early universe, they can manifest themselves in various ways. The simplest
manifestations are as a potentially substantial contribution to the energy density
of the universe or, in the case of magnetic monopoles, as a relic density of
particles carrying magnetic charge. More subtle manifestations are also possible.
For example, relic cosmic strings may act as gravitational lenses or produce
temperature fluctuations in the cosmic microwave background radiation.
DOl: 10.1201/9780367806637-3
65