On a cold day, ice forms quickly on the surface of a pond. But it does
not grow as a smooth, featureless covering. Instead, the water begins
to freeze in many places independently, and the growing plates of ice
join up in random fashion, leaving zig-zag boundaries between
them. These irregular margins are an example of what physicists call
"topological defects" - *defects* because they are places where
the crystal structure of the ice is disrupted, and *topological*
because an accurate description of them involves ideas of symmetry
embodied in topology, the branch of mathematics that focuses on the
study of continuous surfaces.

Current theories of particle physics likewise predict that a variety of topological defects would almost certainly have formed during the early evolution of the universe. Just as water turns to ice (a phase transition) when the temperature drops, so the interactions between elementary particles run through distinct phases as the typical energy of those particles falls with the expansion of the universe. When conditions favor the appearance of a new phase, it generally crops up in many places at the same time, and when separate regions of the new phase run into each other, topological defects are the result. The detection of such structures in the modern universe would provide precious information on events in the earliest instants after the Big Bang. Their absence, on the other hand, would force a major revision of current physical theories.

The aim of this set of Lectures is to introduce the reader to the
subject of topological defects in cosmology. We begin with a review of
the basics of defect formation and evolution, to get a grasp of the
overall picture. We will see that defects are generically predicted
to exist in most interesting models of high energy physics trying to
describe the early universe. The basic elements of the standard
cosmology, with its successes and shortcomings, are covered elsewhere
in this volume, so we will not devote much space to them here. We
will then focus on some specific topics. We will first treat
conducting cosmic strings and one of their most important predictions
for cosmology, namely, the existence of equilibrium configurations of
string loops, dubbed vortons. We will then pass on to study some key
signatures that a network of defects would produce on the cosmic
microwave background (CMB) radiation, *e.g.*, the CMB bispectrum of the
temperature anisotropies from a simulated model of cosmic strings.
Miscellaneous topics also reviewed below are, for example, the way in
which these cosmic entities lead to large-scale structure formation
and some astrophysical footprints left by the various defects, and we
will discuss the possibility of isolating their effects by
astrophysical observations. Also, we will briefly consider
gravitational radiation from strings, as well as the relation of
cosmic defects to the well-known defects formed in condensed-matter
systems like liquid crystals, etc.

Many areas of modern research directly related to cosmic defects are
not covered in these notes. The subject has grown so wide, so fast,
that the best thing we can do is to refer the reader to some of the
excellent recent literature already available. So, have a look, for
example, to the report by
Achucarro & Vachaspati
[2000]
for a treatment of semilocal and electroweak strings
^{(2)} and to
[Vachaspati, 2001]
for a review of certain topological defects, like monopoles,
domain walls and, again, electroweak strings, virtually not covered
here. For conducting defects, cosmic strings in particular, see for
example [Gangui &
Peter, 1998]
for a brief overview of many different
astrophysical and cosmological phenomena, and the comprehensive
colorful lecture notes by
Carter [1997]
on the dynamics of branes
with applications to conducting cosmic strings and vortons. If your
are in cosmological structure formation,
Durrer [2000]
presents a good
review of modern developments on global topological defects and their
relation to CMB anisotropies, while
Magueijo &
Brandenberger [2000]
give a set of imaginative lectures with an update on local string
models of large-scale structure formation and also baryogenesis with
cosmic defects.

If you ever wondered whether you could have a pocket device, the size
of a cellular phone say, to produce "topological defects" on demand
[Chuang, 1994],
then the proceedings of the school held *aux*
Houches on topological defects and non-equilibrium dynamics, edited by
Bunkov & Godfrin
[2000],
are for you; the ensemble of lectures in
this volume give an exhaustive illustration of the interdisciplinary
of topological defects and their relevance in various fields of
physics, like low-temperature condensed-matter, liquid crystals,
astrophysics and high-energy physics.

Finally, all of the above (and more) can be found in the concise review by Hindmarsh & Kibble [1995], particularly concerned with the physics and cosmology of cosmic strings, and in the monograph by Vilenkin & Shellard [2000] on cosmic strings and other topological defects.

^{2} Animations of
semilocal and electroweak string formation and evolution
can be found at
http://www.nersc.gov/~borrill/
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