Monopoles on strings

In cosmological scenarios based on grand unification, string theory or braneworlds, many kinds of topological or non-topological defects, including monopoles and cosmic strings, are predicted to be formed in the early universe. Here we review specifically the physics of composite objects involving monopoles tied to strings. There is a wide variety of these, including for example dumbbells and necklaces, depending on how many strings attach to each monopole and on the extent to which the various fluxes are confined to the strings. We also briefly survey the prospects for observing such structures, the existing observational limits, and potential evidence for a cosmological role.

Causality and non-equilibrium second-order phase transitions in inhomogeneous systems

When a second-order phase transition is crossed at fine rate, the evolution of the system stops being adiabatic as a result of the critical slowing down in the neighborhood of the critical point. In systems with a topologically nontrivial vacuum manifold, disparate local choices of the ground state lead to the formation of topological defects. The universality class of the transition imprints a signature on the resulting density of topological defects: It obeys a power law in the quench rate, with an exponent dictated by a combination of the critical exponents of the transition. In inhomogeneous systems the situation is more complicated, as the spontaneous symmetry breaking competes with bias caused by the influence of the nearby regions that already chose the new vacuum. As a result, the choice of the broken symmetry vacuum may be inherited from the neighboring regions that have already entered the new phase. This competition between the inherited and spontaneous symmetry breaking enhances the role of causality, as the defect formation is restricted to a fraction of the system where the front velocity surpasses the relevant sound velocity and phase transition remains effectively homogeneous. As a consequence, the overall number of topological defects can be substantially suppressed. When the fraction of the system is small, the resulting total number of defects is still given by a power law related to the universality class of the transition, but exhibits a more pronounced dependence on the quench rate. This enhanced dependence complicates the analysis but may also facilitate experimental test of defect formation theories.

Kinks and small-scale structure on cosmic strings

We discuss some hitherto puzzling features of the small-scale structure of cosmic strings. We argue that kinks play a key role, and that an important quantity to study is their sharpness distribution. In particular we suggest that for very small scales the two-point correlation function of the string tangent vector varies linearly with the separation and not as a fractional power, as proposed by Polchinski and Rocha [Phys. Rev. D 74, 083504 (2006)]. However, our results are consistent with theirs, because the range of scales to which this linearity applies shrinks as evolution proceeds.