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. In string theory, the universe is either 10- or 11-dimensional, depending on the strength of interactions and the curvature of spacetime.

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.

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.

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.

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.

The standard model of a cosmic string is a geometrical structure with an angle deficit, which thus is in tension and hence has positive mass. In 1995, Visser et al. proposed that cosmic strings could theoretically also exist with angle excesses, and thus negative tension and hence negative mass.

The stability of such exotic matter strings is problematic; however, they suggested that if a negative mass string were to be wrapped around a wormhole in the early universe, such a wormhole could be stabilized sufficiently to exist in the present day.

The violent oscillations of cosmic strings generically lead to the formation of cusps and kinks. These in turn cause parts of the string to pinch off into isolated loops. These loops have a finite lifespan and decay (primarily) via gravitational radiation. This radiation which leads to the strongest signal from cosmic strings may in turn be detectable in gravitational wave observatories. An important open question is to what extent do the pinched off loops backreact or change the initial state of the emitting cosmic string—such backreaction effects are almost always neglected in computations and are known to be important, even for order of magnitude estimates.

Currently the most sensitive bounds on cosmic string parameters come from the non-detection of gravitational waves by Pulsar timing array data. The earthbound Laser Interferometer Gravitational-Wave Observatory (LIGO) and especially the space-based gravitational wave detector Laser Interferometer Space Antenna (LISA) will search for gravitational waves and are likely to be sensitive enough to detect signals from cosmic strings, provided the relevant cosmic string tensions are not too small.

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