(ed.). Gravitational waves (IOP, 2001)(422s).

Topological defects 213This correlation length depends upon the details of the phase transition and istemperature dependent. In any case, since correlations cannot be established atspeed greater than the speed of light, ξ cannot exceed the causal horizon d H , thedistance travelled by light during the lifetime of the universe. In the standardcosmology d H ∼ t and, thus, one hasξ ≤ t cwhere t c is the time at which the phase transition is completed. The actualmagnitude of ξ at the phase transition and afterwards is determined bycomplicated dynamical processes and can be much smaller than this causalityupper bound.Since the field must be continous, on the boundaries between differentcorrelation regions φ leaves the vacuum manifold Å and assume valuescorresponding to a high potential energy. For topological reasons, these regionsof false vacuum are stable and survive to further evolution of the universe frozenin the form of topological defects.The cosmological production mechanism described above is known as theKibble mechanism [32] and is very much akin to the mechanism for productionof various defects in solid state and condensed matter systems. Crystal defects, forexample, form when the water freezes or when a metal crystallizes. The analogiesbetween defects in particle physics and condensed matter physics are quite deep.Defects form for the same reason: the vacuum manifold is topologically nontrivial.However, the defect dynamics is different. The motion of defects incondensed matter are friction-dominated, whereas the defect in cosmology obeyrelativistic equations, second order in time derivatives, since they come from arelativistic field theory.Depending on the topology of the manifold Å the defects can occur inthe form of points, lines or surfaces. They are called monopoles, strings anddomain walls, respectively [32]. Hybrid defects can be formed in a sequence ofphase transitions, for example, the first transition produces monopoles, which getconnected by strings at the second phase transition. The main conclusions of thestudies about these defects can be summarized as follows.• Domain walls and monopoles are disastrous for cosmological models andtheir presence should be avoided.• Strings cause no harm, but can lead to very interesting cosmologicalconsequences. In particular, they can generate density fluctuations sufficientto explain galaxy formation and can produce a number of distinctive andunique observational effects (anisotropies in the CMB temperature, doubleimages of objects behind them and a stochastic GW background).• Hybrid defects are transient and eventually decay into relativistic particles.If this happens at a sufficiently early time, the decay products thermalize andwe can see no trace of the defects, except perhaps in the form of gravitationalwaves.