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

Topological defects 22113.1.2 Hybrid defectsIf the symmetry breaking responsible for the formation of the strings occur as apart of a much more complicated breaking scheme, it is likely that hybrid systemscomposed by topological defects of different dimensionality may form. In thecase when the hybrid system does not annihilate immediately this may lead to astochastic background in a similar way to that for the strings [38]. The interestingfeature of these objects is that they evade the constraints from the CMB and pulsartiming allowing for larger values of Gµ and hence larger contributions to theSGWB in the detectable range of frequencies.Walls bounded by stringsDomain walls are formed when a discrete symmetry is broken. The simplestmodel of this sort is that of real scalar field with a potentialV (φ) = 1 2 λ(φ2 − η 2 w )2 .The reflection symmetry group Z 2 of the Lagrangian (invariance under φ →−φ)is spontaneously broken when φ takes on the VEV 〈φ〉 =±η, and so the manifoldÅ consists of only two points. As we go from a region with 〈φ〉 =η to a regionwith 〈φ〉 =−η, we should necessarily pass through 〈φ〉 =0 and, thus, the tworegions must be separated by a wall of false vacuum. Therefore, the simplestsequence of phase transitions that results in walls bounded by strings isG → H ⊗ Z 2 → Hwhere at first transition (T ∼ η s ) strings form and at the second (T ∼ η w ) eachstring gets attached to a domain wall.Before the formation of walls the evolution of strings is as in the standardscenario described above. After a period of overdamped motion, the stringsstart moving relativistically at time t s and approach a scaling regime where thecharacteristic scale of the network is comparable to the horizon. After the timet w at which the domain walls form the evolution of the network depends on theratio between the string tension µ ∼ ηs 2 and wall surface tension σ ∼ η3 w . Thewalls become dynamically important at t ∼ µ/σ , when they pull the stringstowards one another, and the network breaks into pieces of wall bounded by string.Alternatively, if t w >µ/σthe breakup of the network occurs immediately afterthe wall formation. By indicating with t ∗ = max{µ/σ, t w }, the typical size of thepieces is expected to be ∼αt ∗ .Gravitational waves emitted by oscillating loop of strings during the periodt ∈ (t s , t ∗ ) form a SGWB with a nearly flat spectrum extending over thefrequency range f ∈ [2/α(t ∗ t eq ) 1/2 , 2/α(t s t eq ) 1/2 ]. For this frequency rangeto overlap with the one covered by VIRGO the strings must decay before thedecoupling, and, thus, the only constraint on this background comes from big