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{{short description|Speculative feature of the early universe}}
{{distinguish|text=[[String (physics)
'''Cosmic strings''' are hypothetical 1-dimensional [[topological defect]]s which may have formed during a [[Symmetry breaking|symmetry-breaking]] [[cosmological phase transition|phase transition]] in the early universe when the [[topology]] of the [[Vacuum state|vacuum]] manifold associated to this symmetry breaking was not [[Simply connected space|simply connected]].
In 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]].
==Theories containing cosmic strings==
In string theory, the role of cosmic strings can be played by the fundamental strings (or F-strings) themselves that define the theory [[Perturbation theory|perturbatively]], by D-strings which are related to the F-strings by weak-strong or so called [[S-duality]], or higher-dimensional [[D-branes|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.<ref>{{cite journal |arxiv=hep-th/0312067 |bibcode=2004JHEP...06..013C |doi=10.1088/1126-6708/2004/06/013 |title=Cosmic F- and D-strings |year=2004 |last1=Copeland |first1=Edmund J |last2=Myers |first2=Robert C |last3=Polchinski |first3=Joseph |journal=Journal of High Energy Physics |volume=2004 |issue=6 |pages=013|s2cid=140465 }}</ref>▼
The prototypical example of a
▲In
==Dimensions==
Cosmic strings, if they exist, would be extremely thin [[topological defect]]s with diameters of the same order of magnitude as that of a proton, i.e. {{nobreak|~
In field theory, the string width is set by the scale of the symmetry
==Gravitation==
{{refimprove section|date=September 2016}}
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°. <ref>{{cite journal| last=Gott| first=J. Richard| title=Closed timelike curves produced by pairs of moving cosmic strings: Exact solutions| journal=Phys. Rev. Lett.| date=1991| volume=66| issue=9| pages=1126–1129| doi=10.1103/PhysRevLett.66.1126| pmid=10044002| bibcode=1991PhRvL..66.1126G}}</ref> 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.{{clarify|date=September 2019}}
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===Negative mass cosmic string===
The [[Standard Model|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, [[Matt Visser|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.<ref>{{cite journal |arxiv=astro-ph/9409051 |bibcode=1995PhRvD..51.3117C |doi=10.1103/PhysRevD.51.3117 |pmid=10018782 |title=Natural wormholes as gravitational lenses |year=1995 |last1=Cramer |first1=John |last2=Forward |first2=Robert |last3=Morris |first3=Michael |last4=Visser |first4=Matt |last5=Benford |first5=Gregory |last6=Landis |first6=Geoffrey |journal=Physical Review D |volume=51 |issue=6 |pages=3117–3120|s2cid=42837620 }}</ref><ref>{{cite press release |url=http://www.geoffreylandis.com/wormholes.htp |title=Searching for a 'Subway to the Stars' |url-status=dead |archive-url=https://web.archive.org/web/20120415100921/http://www.geoffreylandis.com/wormholes.htp |archive-date=2012-04-15 }}</ref>
===Super-critical cosmic string===
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The violent oscillations of cosmic strings generically lead to the formation of [[Cusp (singularity)|cusps]] and [[Sine-Gordon equation#Soliton solutions|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 observatory|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.
[[Gravitational lensing]] of a galaxy by a straight section of a cosmic string would produce two identical, undistorted images of the galaxy. In 2003 a group led by
A piece of evidence supporting cosmic string theory is a phenomenon noticed in observations of the "double [[quasar]]" called [[Twin Quasar|Q0957+561A,B]]. Originally discovered by [[Dennis Walsh]], Bob Carswell, and [[Ray Weymann]] in 1979, the double image of this quasar is caused by a galaxy positioned between it and the Earth. The [[gravitational lens]] effect of this intermediate galaxy bends the quasar's light so that it follows two paths of different lengths to Earth. The result is that we see two images of the same quasar, one arriving a short time after the other (about 417.1 days later). However, a team of astronomers at the [[Harvard-Smithsonian Center for Astrophysics]] led by [[Rudolph Schild]] studied the quasar and found that during the period between September 1994 and July 1995 the two images appeared to have no time delay; changes in the brightness of the two images occurred simultaneously on four separate occasions. Schild and his team believe that the only explanation for this observation is that a cosmic string passed between the Earth and the quasar during that time period traveling at very high speed and oscillating with a period of about 100 days.<ref>{{cite journal |arxiv=astro-ph/0406434 |bibcode=2004A&A...422..477S|doi=10.1051/0004-6361:20040274 |title=Anomalous fluctuations in observations of Q0957+561 A,B: Smoking gun of a cosmic string? |year=2004 |last1=Schild |first1=R. |last2=Masnyak |first2=I. S. |last3=Hnatyk |first3=B. I. |last4=Zhdanov |first4=V. I. |journal=Astronomy and Astrophysics |volume=422 |issue=2 |pages=477–482|s2cid=16939392}}</ref>
==String theory and cosmic strings==
{{refimprove section|date=September 2016}}
During the early days of string theory both string theorists and cosmic string theorists believed that there was no direct connection between [[superstrings]] and cosmic strings (the names were chosen independently by analogy with [[twine|ordinary string]]). The possibility of cosmic strings being produced in the early universe was first envisioned by quantum field theorist [[Tom Kibble]] in 1976,<ref name="Kibble 1976" /> and this sprouted the first flurry of interest in the field.
In 1985, during the [[first superstring revolution]], [[Edward Witten]] contemplated on the possibility of fundamental superstrings having been produced in the early universe and stretched to macroscopic scales, in which case (following the nomenclature of Tom Kibble) they would then be referred to as cosmic superstrings.<ref name="witten-cosmic-superstrings">{{cite journal |last1=Witten |first1=Edward |title=Cosmic Superstrings |journal=Phys. Lett. B |date=1985 |volume=153 |issue=4–5 |pages=243–246 |doi=10.1016/0370-2693(85)90540-4|bibcode=1985PhLB..153..243W }}</ref> He concluded that had they been produced they would have either disintegrated into smaller strings before ever reaching macroscopic scales (in the case of [[Type I superstring]] theory), they would always appear as boundaries of [[Domain wall (string theory)|___domain walls]] whose tension would force the strings to collapse rather than grow to cosmic scales (in the context of [[Heterotic string|heterotic superstring]] theory), or having a characteristic energy scale close to the [[Planck energy]] they would be produced before [[cosmological inflation]] and hence be diluted away with the expansion of the universe and not be observable.
Much has changed since these early days, primarily due to the [[second superstring revolution]]. It is now known that string theory in addition to the fundamental strings which define the theory perturbatively also contains other one-dimensional objects, such as D-strings, and higher-dimensional objects such as D-branes, NS-branes and M-branes partially wrapped on compact internal spacetime dimensions, while being spatially extended in one non-compact dimension. The possibility of [[Large extra dimension|large compact dimensions]] and large [[Randall–Sundrum model|warp factors]] allows strings with tension much lower than the Planck scale. 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.▼
▲Much has changed since these early days, primarily due to the [[second superstring revolution]]. It is now known that string theory contains, in addition to the fundamental strings which define the theory perturbatively
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 cosmology|brane inflation]],<ref>{{cite journal |arxiv=hep-th/0204074 |bibcode=2002PhLB..536..185S |doi=10.1016/S0370-2693(02)01824-5 |title=Cosmic string production towards the end of brane inflation |year=2002 |last1=Sarangi |first1=Saswat |last2=Tye |first2=S.-H.Henry |journal=Physics Letters B |volume=536 |issue=3–4 |pages=185|s2cid=14274241 }}</ref> 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.
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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.<ref>{{Cite journal|last1=Movahed|first1=M. Sadegh|last2=Javanmardi|first2=B.|last3=Sheth|first3=Ravi K.|date=2013-10-01|title=Peak–peak correlations in the cosmic background radiation from cosmic strings|url=https://academic.oup.com/mnras/article/434/4/3597/965202|journal=Monthly Notices of the Royal Astronomical Society|language=en|volume=434|issue=4|pages=3597–3605|doi=10.1093/mnras/stt1284|doi-access=free |issn=0035-8711|arxiv=1212.0964|bibcode=2013MNRAS.434.3597M|s2cid=53499674}}</ref><ref>{{Cite journal|last1=Vafaei Sadr|first1=A|last2=Movahed|first2=S M S|last3=Farhang|first3=M|last4=Ringeval|first4=C|last5=Bouchet|first5=F R|date=2017-12-14|title=A Multiscale pipeline for the search of string-induced CMB anisotropies|journal=Monthly Notices of the Royal Astronomical Society|language=en|volume=475|issue=1|pages=1010–1022|doi=10.1093/mnras/stx3126|doi-access=free|issn=0035-8711|arxiv=1710.00173|bibcode=2018MNRAS.475.1010V|s2cid=5825048}}</ref><ref>{{Cite journal|last1=Vafaei Sadr|first1=A|last2=Farhang|first2=M|last3=Movahed|first3=S M S|last4=Bassett|first4=B|last5=Kunz|first5=M|date=2018-05-01|title=Cosmic string detection with tree-based machine learning|journal=Monthly Notices of the Royal Astronomical Society|language=en|volume=478|issue=1|pages=1132–1140|doi=10.1093/mnras/sty1055|doi-access=free|issn=0035-8711|arxiv=1801.04140|bibcode=2018MNRAS.478.1132V|s2cid=53330913}}</ref>
== Potential applications ==
In 1986, [[John G. Cramer]] proposed that spacecraft equipped with magnet coils could travel along cosmic strings, analogous to how a [[maglev]] train travels along a rail line.<ref>{{Cite web |title=Alternate View Column AV-19 |url=https://www.npl.washington.edu/av/altvw19.html |access-date=2024-08-15 |website=www.npl.washington.edu}}</ref>
==See also==
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* [https://www.youtube.com/watch?v=D3IDL8lfTeA A simulation of cosmic string]
* http://www.damtp.cam.ac.uk/user/gr/public/cs_interact.html
* {{cite journal |arxiv=astro-ph/0302547 |bibcode=2003MNRAS.343..353S |doi=10.1046/j.1365-8711.2003.06568.x |title=CSL-1: Chance projection effect or serendipitous discovery of a gravitational lens induced by a cosmic string? |year=2003 |last1=Sazhin |first1=M. |last2=Longo |first2=G. |last3=Capaccioli |first3=M. |last4=Alcala |first4=J. M. |last5=Silvotti |first5=R. |last6=Covone |first6=G. |last7=Khovanskaya |first7=O. |last8=Pavlov |first8=M. |last9=Pannella |first9=M. |journal=Monthly Notices of the Royal Astronomical Society |volume=343 |issue=2 |pages=353|display-authors=9 |last10=Radovich |first10=M. |last11=Testa |first11=V. |doi-access=free |s2cid=18650564 }}
* {{cite journal |arxiv=astro-ph/0406434 |bibcode=2004A&A...422..477S |doi=10.1051/0004-6361:20040274 |title=Anomalous fluctuations in observations of Q0957+561 A,B: Smoking gun of a cosmic string? |year=2004 |last1=Schild |first1=R. |last2=Masnyak |first2=I. S. |last3=Hnatyk |first3=B. I. |last4=Zhdanov |first4=V. I. |journal=Astronomy and Astrophysics |volume=422 |issue=2 |pages=477–482|s2cid=16939392 }}
* {{cite arXiv |eprint=astro-ph/0410073 |last1=Kibble |first1=T. W. B. |title=Cosmic strings reborn? |year=2004}}
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* [http://xstructure.inr.ac.ru/x-bin/theme3.py?level=1&index1=443810 Cosmic strings and superstrings on arxiv.org]
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