Related papers: Cosmic Structure Formation with Topological Defect…
Lars Onsager and Richard Feynman envisioned that the three-dimensional (3D) superfluid-to-normal $\lambda$ transition in $^{4}$He occurs through the proliferation of vortices. This process should hold for every phase transition in the same…
The standard theory of cosmic structure formation posits that the present-day rich structure of the Universe developed through gravitational amplification of tiny matter density fluctuations generated in its very early history. Recent…
Spin-mass vortices have been observed to form in rotating superfluid 3He-B following the absorption of a thermal neutron and a rapid transition from the normal to superfluid state. The spin-mass vortex is a composite defect which consists…
Topological defects arise in a variety of systems, e.g. vortices in superfluid helium to cosmic strings in the early universe. There is an indirect evidence of neutron superfluid vortices from glitches in pulsars. One also expects that…
Formation of topological defects during symmetry breaking phase transitions via the {\it Kibble mechanism} is extensively used in systems ranging from condensed matter physics to the early stages of the universe. Kibble mechanism uses…
The formation of topological defects during continuous second-order phase transitions is well described by the Kibble-Zurek mechanism (KZM). However, when the spontaneously broken symmetry is only approximate, such transitions become smooth…
We discuss the origin of topological defects in phase transitions and analyze their role as a "diagnostic tool" in the study of the non-equilibrium dynamics of symmetry breaking. Homogeneous second order phase transitions are the focus of…
The topology of space is usually assumed simply connected, but could be multi-connected. We review in the latter case the possibility that topological defects arising at high energy phase transitions might still be present and find that…
An introduction to topological defects in cosmology is given. We discuss their possible relevance for structure formation. Especial emphasis is given on the signature of topological defects in the spectrum of anisotropies in the cosmic…
Combination of topology and general relativity can lead to some profound and farsighted predictions. It is well known that symmetry breaking of the Higgs vacuum field in the early universe possibly induced topological defects in spacetime,…
During the past two decades, cosmologists turned to particle physics in order to explore the physics of the very early Universe. The main link between the physics of the smallest and largest structures in the Universe is the idea of…
This is a survey article for the Encyclopedia of Mathematical Physics, 2nd Edition. Topological defects are described in the context of the 2-dimensional Ising model on the lattice, in 2-dimensional quantum field theory, in topological…
In cosmological first-order phase transitions, the progress of true-vacuum bubbles is expected to be significantly retarded by the interaction between the bubble wall and the hot plasma. It has been claimed that this leads to a significant…
This article reviews the prevailing paradigm for how galaxies and larger structures formed in the universe: gravitational instability. Basic observational facts are summarized to motivate the standard cosmological framework underlying most…
We study random bubble lattices which can be produced by processes such as first order phase transitions, and derive characteristics that are important for understanding the percolation of distinct varieties of bubbles. The results are…
The topological theory and the Volterra process are key tools for the classification of defects in Condensed Mater Physics. We employ the same methods to classify the 2D defects of a 4D maximally symmetric spacetime. These \textit{cosmic…
We discuss the structure of topological defects in the context of extra dimensions where the symmetry breaking terms are localized. These defects develop structure in the extra dimension which differs from the case where symmetry breaking…
Symmetry breaking phase transitions play an important role in nature. When a system traverses such a transition at a finite rate, its causally disconnected regions choose the new broken symmetry state independently. Where such local choices…
In this paper we review the hypothesis that a considerable part of the cosmic ray flux observed above about $10^{19}\eV$ may be produced by decaying or annihilating topological defects left over from phase transitions in the early universe…
The formation of topological defects in a second order phase transition in the early universe is an out-of-equilibrium process. Condensed matter experiments seem to support Zurek's mechanism, in which the freezing of thermal fluctuations…