**1.4. A survey of topological defects**

Different models for the Higgs field lead to the formation of a whole
variety of topological defects, with very different characteristics
and dimensions. Some of the proposed theories have symmetry breaking
patterns leading to the formation of `domain walls' (mirror reflection
discrete symmetry): incredibly thin planar surfaces trapping enormous
concentrations of mass-energy which separate domains of conflicting
field orientations, similar to two-dimensional sheet-like structures
found in ferromagnets. Within other theories, cosmological fields get
distributed in such a way that the old (symmetric) phase gets confined
into a finite region of space surrounded completely by the new
(non-symmetric) phase. This situation leads to the generation of
defects with linear geometry called `cosmic strings'. Theoretical
reasons suggest these strings (vortex lines) do not have any loose
ends in order that the two phases not get mixed up. This leaves
infinite strings and closed loops as the only possible alternatives
for these defects to manifest themselves in the early
universe ^{(4)}.

With a bit more abstraction scientists have even conceived other (semi) topological defects, called `textures'. These are conceptually simple objects, yet, it is not so easy to imagine them for they are just global field configurations living on a three-sphere vacuum manifold (the minima of the effective potential energy), whose non linear evolution perturbs spacetime. Turok [1989] was the first to realize that many unified theories predicted the existence of peculiar Higgs field configurations known as (texture) knots, and that these could be of potential interest for cosmology. Several features make these defects interesting. In contrast to domain walls and cosmic strings, textures have no core and thus the energy is more evenly distributed over space. Secondly, they are unstable to collapse and it is precisely this last feature which makes these objects cosmologically relevant, for this instability makes texture knots shrink to a microscopic size, unwind and radiate away all their energy. In so doing, they generate a gravitational field that perturbs the surrounding matter in a way which can seed structure formation.

^{4} `Monopole' is another possible
topological defect;
we defer its discussion to the next subsection. Cosmic strings
bounded by monopoles is yet another possibility in GUT phase
transitions of the kind, *e.g.*, **G**
**K** × *U*(1)
**K**. The
first transition yields monopoles carrying a magnetic charge
of the *U*(1) gauge field, while in the second transition the magnetic
field in squeezed into flux tubes connecting monopoles and antimonopoles
[Langacker & Pi,
1980].
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