Cosmic string
This article may be too technical for most readers to understand.(May 2021) |
Cosmic strings are hypothetical 1-dimensional
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
Theories containing cosmic strings
The prototypical example of a field theory with cosmic strings is the
In
Dimensions
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
Gravitation
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A string is a geometrical deviation from
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.[clarification needed]
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
Negative mass cosmic string
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.[4][5]
Super-critical cosmic string
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The exterior geometry of a (straight) cosmic string can be visualized in an embedding diagram as follows: Focusing on the two-dimensional surface perpendicular to the string, its geometry is that of a cone which is obtained by cutting out a wedge of angle δ and gluing together the edges. The angular deficit δ is linearly related to the string tension (= mass per unit length), i.e. the larger the tension, the steeper the cone. Therefore, δ reaches 2π for a certain critical value of the tension, and the cone degenerates to a cylinder. (In visualizing this setup one has to think of a string with a finite thickness.) For even larger, "super-critical" values, δ exceeds 2π and the (two-dimensional) exterior geometry closes up (it becomes compact), ending in a conical singularity.
However, this static geometry is unstable in the super-critical case (unlike for sub-critical tensions): Small perturbations lead to a dynamical spacetime which expands in axial direction at a constant rate. The 2D exterior is still compact, but the conical singularity can be avoided, and the embedding picture is that of a growing cigar. For even larger tensions (exceeding the critical value by approximately a factor of 1.6), the string cannot be stabilized in radial direction anymore.[6]
Realistic cosmic strings are expected to have tensions around 6 orders of magnitude below the critical value, and are thus always sub-critical. However, the inflating cosmic string solutions might be relevant in the context of brane cosmology, where the string is promoted to a 3-brane (corresponding to our universe) in a six-dimensional bulk.
Observational evidence
It was once thought that the gravitational influence of cosmic strings might contribute to the
The violent oscillations of cosmic strings generically lead to the formation of
A piece of evidence supporting cosmic string theory is a phenomenon noticed in observations of the "double
Currently the most sensitive bounds on cosmic string parameters come from the non-detection of gravitational waves by pulsar timing array data.[13] 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.
String theory and cosmic strings
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During the early days of string theory both string theorists and cosmic string theorists believed that there was no direct connection between
In 1985, during the
Much has changed since these early days, primarily due to the
Furthermore, various dualities that have been discovered point to the conclusion that actually all these apparently different types of string are just the same object as it appears in different regions of parameter space. These new developments have largely revived interest in cosmic strings, starting in the early 2000s.
In 2002, Henry Tye and collaborators predicted the production of cosmic superstrings during the last stages of brane inflation,[15] a string theory construction of the early universe that gives leads to an expanding universe and cosmological inflation. It was subsequently realized by string theorist Joseph Polchinski that the expanding Universe could have stretched a "fundamental" string (the sort which superstring theory considers) until it was of intergalactic size. Such a stretched string would exhibit many of the properties of the old "cosmic" string variety, making the older calculations useful again. As theorist Tom Kibble remarks, "string theory cosmologists have discovered cosmic strings lurking everywhere in the undergrowth". Older proposals for detecting cosmic strings could now be used to investigate superstring theory.
Superstrings, D-strings or the other stringy objects mentioned above stretched to intergalactic scales would radiate gravitational waves, which could be detected using experiments like LIGO and especially the space-based gravitational wave experiment LISA. They might also cause slight irregularities in the cosmic microwave background, too subtle to have been detected yet but possibly within the realm of future observability.
Note that most of these proposals depend, however, on the appropriate cosmological fundamentals (strings, branes, etc.), and no convincing experimental verification of these has been confirmed to date. Cosmic strings nevertheless provide a window into string theory. If cosmic strings are observed, which is a real possibility for a wide range of cosmological string models, this would provide the first experimental evidence of a string theory model underlying the structure of spacetime.
Cosmic string network
There are many attempts to detect the footprint of a cosmic strings network.[16][17][18]
See also
- 0-dimensional topological defect: magnetic monopole
- 2-dimensional topological defect: domain wall (e.g. of 1-dimensional topological defect: a cosmic string)
- Cosmic string loop stabilised by a fermionic supercurrent: vorton
References
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External links
- An artistic perspective of Cosmic Strings
- A simulation of cosmic string
- http://www.damtp.cam.ac.uk/user/gr/public/cs_interact.html
- Sazhin, M.; Longo, G.; Capaccioli, M.; Alcala, J. M.; Silvotti, R.; Covone, G.; Khovanskaya, O.; Pavlov, M.; Pannella, M.; et al. (2003). "CSL-1: Chance projection effect or serendipitous discovery of a gravitational lens induced by a cosmic string?". Monthly Notices of the Royal Astronomical Society. 343 (2): 353. S2CID 18650564.
- Schild, R.; Masnyak, I. S.; Hnatyk, B. I.; Zhdanov, V. I. (2004). "Anomalous fluctuations in observations of Q0957+561 A,B: Smoking gun of a cosmic string?". Astronomy and Astrophysics. 422 (2): 477–482. S2CID 16939392.
- Kibble, T. W. B. (2004). "Cosmic strings reborn?". arXiv:astro-ph/0410073.
- Lo, Amy S.; Wright, Edward L. (2005). "Signatures of Cosmic Strings in the Cosmic Microwave Background". arXiv:astro-ph/0503120.
- Sazhin, M.; Capaccioli, M.; Longo, G.; Paolillo, M.; Khovanskaya, O. (2006). "Further Spectroscopic Observations of the CSL 1 Object". The Astrophysical Journal. 636 (1): L5–L8. S2CID 10176938.
- Agol, Eric; Hogan, Craig; Plotkin, Richard (2006). "Hubble imaging excludes cosmic string lens". Physical Review D. 73 (8): 87302. S2CID 119450257.
- Dr. Kip Thorne, ITP & Caltech. Spacetime Warps and the Quantum: A Glimpse of the Future. Lecture slides and audio
- Cosmic strings and superstrings on arxiv.org