Cosmic string

Cosmic strings are hypothetical 1-dimensional topological defects which may have formed during a symmetry breaking phase transition in the early universe when the topology of the vacuum manifold associated to this symmetry breaking was not simply connected. It is expected that at least one string per Hubble volume is formed. Their existence was first contemplated by the theoretical physicist Tom Kibble in the 1970s. Cosmic strings are hypothetical 1-dimensional topological defects which may have formed during a symmetry breaking phase transition in the early universe when the topology of the vacuum manifold associated to this symmetry breaking was not simply connected. It is expected that at least one string per Hubble volume is formed. Their existence was first contemplated by the theoretical physicist Tom Kibble in the 1970s. The formation of cosmic strings is somewhat analogous to the imperfections that form between crystal grains in solidifying liquids, or the cracks that form when water freezes into ice. The phase transitions leading to the production of cosmic strings are likely to have occurred during the earliest moments of the universe's evolution, just after cosmological inflation, and are a fairly generic prediction in both quantum field theory and string theory models of the early universe. In string theory, the role of cosmic strings can be played by the fundamental strings (or F-strings) themselves that define the theory perturbatively, by D-strings which are related to the F-strings by weak-strong or so called S-duality, or higher-dimensional D-, NS- or M-branes that are partially wrapped on compact cycles associated to extra spacetime dimensions so that only one non-compact dimension remains. The prototypical example of a quantum field theory with cosmic strings is the Abelian Higgs model. The quantum field theory and string theory cosmic strings are expected to have many properties in common, but more research is needed to determine the precise distinguishing features. The F-strings for instance are fully quantum-mechanical and do not have a classical definition, whereas the field theory cosmic strings are almost exclusively treated classically. Cosmic strings, if they exist, would be extremely thin with diameters of the same order of magnitude as that of a proton, i.e. ~ 1 fm, or smaller. Given that this scale is much smaller than any cosmological scale these strings are often studied in the zero-width, or Nambu–Goto approximation. Under this assumption strings behave as one-dimensional objects and obey the Nambu–Goto action, which is classically equivalent to the Polyakov action that defines the bosonic sector of superstring theory. In field theory, the string width is set by the scale of the symmetry breaking phase transition. In string theory, the string width is set (in the simplest cases) by the fundamental string scale, warp factors (associated to the spacetime curvature of an internal six-dimensional spacetime manifold) and/or the size of internal compact dimensions. (In string theory, the universe is either 10- or 11-dimensional, depending on the strength of interactions and the curvature of spacetime.) A string is a geometrical deviation from Euclidean geometry in spacetime characterized by an angular deficit: a circle around the outside of a string would comprise a total angle less than 360°. From the general theory of relativity such a geometrical defect must be in tension, and would be manifested by mass. Even though cosmic strings are thought to be extremely thin, they would have immense density, and so would represent significant gravitational wave sources. A cosmic string about a kilometer in length may be more massive than the Earth. However general relativity predicts that the gravitational potential of a straight string vanishes: there is no gravitational force on static surrounding matter. The only gravitational effect of a straight cosmic string is a relative deflection of matter (or light) passing the string on opposite sides (a purely topological effect). A closed cosmic string gravitates in a more conventional way. During the expansion of the universe, cosmic strings would form a network of loops, and in the past it was thought that their gravity could have been responsible for the original clumping of matter into galactic superclusters. It is now calculated that their contribution to the structure formation in the universe is less than 10%.