1.1. How defects form
A central concept of particle physics theories attempting to unify all the fundamental interactions is the concept of symmetry breaking. As the universe expanded and cooled, first the gravitational interaction, and subsequently all other known forces would have begun adopting their own identities. In the context of the standard hot Big Bang theory the spontaneous breaking of fundamental symmetries is realized as a phase transition in the early universe. Such phase transitions have several exciting cosmological consequences and thus provide an important link between particle physics and cosmology.
There are several symmetries which are expected to break down in the course of time. In each of these transitions the space-time gets `oriented' by the presence of a hypothetical force field called the `Higgs field', named for Peter Higgs, pervading all the space. This field orientation signals the transition from a state of higher symmetry to a final state where the system under consideration obeys a smaller group of symmetry rules. As an every-day analogy we may consider the transition from liquid water to ice; the formation of the crystal structure ice (where water molecules are arranged in a well defined lattice), breaks the symmetry possessed when the system was in the higher temperature liquid phase, when every direction in the system was equivalent. In the same way, it is precisely the orientation in the Higgs field which breaks the highly symmetric state between particles and forces.
Having built a model of elementary particles and forces, particle physicists and cosmologists are today embarked on a difficult search for a theory that unifies all the fundamental interactions. As we mentioned, an essential ingredient in all major candidate theories is the concept of symmetry breaking. Experiments have determined that there are four physical forces in nature; in addition to gravity these are called the strong, weak and electromagnetic forces. Close to the singularity of the hot Big Bang, when energies were at their highest, it is believed that these forces were unified in a single, all-encompassing interaction. As the universe expanded and cooled, first the gravitational interaction, then the strong interaction, and lastly the weak and the electromagnetic forces would have broken out of the unified scheme and adopted their present distinct identities in a series of symmetry breakings.
Theoretical physicists are still struggling to understand how gravity can be united with the other interactions, but for the unification of the strong, weak and electromagnetic forces plausible theories exist. Indeed, force-carrying particles whose existence demonstrated the fundamental unification of the weak and electromagnetic forces into a primordial "electroweak" force - the W and Z bosons - were discovered at CERN, the European accelerator laboratory, in 1983. In the context of the standard Big Bang theory, cosmological phase transitions are produced by the spontaneous breaking of a fundamental symmetry, such as the electroweak force, as the universe cools. For example, the electroweak interaction broke into the separate weak and electromagnetic forces when the observable universe was 10-12 seconds old, had a temperature of 1015 degrees Kelvin, and was only one part in 1015 of its present size. There are also other phase transitions besides those associated with the emergence of the distinct forces. The quark-hadron confinement transition, for example, took place when the universe was about a microsecond old. Before this transition, quarks - the particles that would become the constituents of the atomic nucleus - moved as free particles; afterward, they became forever bound up in protons, neutrons, mesons and other composite particles.
As we said, the standard mechanism for breaking a symmetry involves the hypothetical Higgs field that pervades all space. As the universe cools, the Higgs field can adopt different ground states, also referred to as different vacuum states of the theory. In a symmetric ground state, the Higgs field is zero everywhere. Symmetry breaks when the Higgs field takes on a finite value (see Figure 1.1).
Figure 1. Temperature-dependent effective potential for a first-order phase transition for the Higgs field. For very high temperatures, well above the critical one Tc, the potential possesses just one minimum for the vanishing value of the Higgs field. Then, when the temperature decreases, a whole set of minima develops (it may be two or more, discrete or continuous, depending of the type of symmetry under consideration). Below Tc, the value = 0 stops being the global minimum and the system will spontaneously choose a new (lower) one, say = exp(i) (for complex ) for some angle and nonvanishing , amongst the available ones. This choice signals the breakdown of the symmetry in a cosmic phase transition and the generation of random regions of conflicting field orientations . In a cosmological setting, the merging of these domains gives rise to cosmic defects.
Kibble  first saw the possibility of defect formation when he realized that in a cooling universe phase transitions proceed by the formation of uncorrelated domains that subsequently coalesce, leaving behind relics in the form of defects. In the expanding universe, widely separated regions in space have not had enough time to `communicate' amongst themselves and are therefore not correlated, due to a lack of causal contact. It is therefore natural to suppose that different regions ended up having arbitrary orientations of the Higgs field and that, when they merged together, it was hard for domains with very different preferred directions to adjust themselves and fit smoothly. In the interfaces of these domains, defects form. Such relic `flaws' are unique examples of incredible amounts of energy and this feature attracted the minds of many cosmologists.