The structure of cosmic strings

The topic of cosmic strings provides a bridge between the physics of the very small and the very large. They are predicted by some unified theories of particle interactions. If they exist, they may help to explain some of the largest-scale structures seen in the Universe today. They are `topological defects' that may have been formed at phase transitions in the very early history of the Universe, analogous to those found in some condensed-matter systems --- vortex lines in liquid helium, flux tubes in type-II superconductors, or disclination lines in liquid crystals. In this review, we describe what they are, why they have been hypothesized and what their cosmological implications would be. The relevant background from the standard models of particle physics and cosmology is described in section 1. In section 2, we review the idea of symmetry breaking in field theories, and show how the defects formed are constrained by the topology of the manifold of degenerate vacuum states. We also discuss the different types of cosmic strings that can appear in different field theories. Section 3 is devoted to the dynamics of cosmic strings, and section 4 to their interaction with other fields. The formation and evolution of cosmic strings in the early Universe is the subject of section 5, while section 6 deals with their observational implications. Finally, the present status of the theory is reviewed in section 7.

By investigating the canonical commutation rules for gravitating quantized particles in a 2+1 dimensional world it is found that these particles live on a space-time lattice. The space-time lattice points can be characterized by three integers. Various representations are possible, the details depending on the topology chosen for energy-momentum space. We find that an \(S_2\times S_1\) topology yields a physically most interesting lattice within which first quantization of Dirac particles is possible. An \(S_3\) topology also gives a lattice, but does not allow first quantized particles.

A new method is presented for assigning distributional curvature, in an invariant manner, to a space-time of low differentiability, using the techniques of Colombeau's `new generalised functions'. The method is applied to show that curvature of a cone is equivalent to a delta function. The same is true under small enough perturbations.