Cosmic string: Difference between revisions

Revision as of 22:03, 15 September 2020

Revision as of 11:02, 19 September 2020

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==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 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.

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===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, [[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 |url=http://www.geoffreylandis.com/wormholes.htp |title=Searching for a 'Subway to the Stars' |url-status=dead |archiveurl=https://web.archive.org/web/20120415100921/http://www.geoffreylandis.com/wormholes.htp |archivedate=2012-04-15 }}</ref>

===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.<ref>{{cite journal|last1=Niedermann|first1=Florian|last2=Schneider|first2=Robert|title=Radially stabilized inflating cosmic strings|journal=Phys. Rev. D|date=2015|volume=91|issue=6|page=064010|doi=10.1103/PhysRevD.91.064010|arxiv = 1412.2750 |bibcode = 2015PhRvD..91f4010N |s2cid=118411378}}</ref>

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.

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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 [[Mikhail Sazhin]] reported the accidental discovery of two seemingly identical galaxies very close together in the sky, leading to speculation that a cosmic string had been found.<ref>{{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. |s2cid=18650564 }}</ref> However, observations by the [[Hubble Space Telescope]] in January 2005 showed them to be a pair of similar galaxies, not two images of the same galaxy.<ref>{{cite journal |arxiv=astro-ph/0603838 |bibcode=2006PhRvD..73h7302A |doi=10.1103/PhysRevD.73.087302 |title=Hubble imaging excludes cosmic string lens |year=2006 |last1=Agol |first1=Eric |last2=Hogan |first2=Craig |last3=Plotkin |first3=Richard |journal=Physical Review D |volume=73 |issue=8|pages=87302 |s2cid=119450257 }}</ref><ref>{{cite arXiv |eprint=astro-ph/0601494 |last1=Sazhin |first1=M. V. |last2=Capaccioli |first2=M. |last3=Longo |first3=G. |last4=Paolillo |first4=M. |last5=Khovanskaya |first5=O. S. |last6=Grogin |first6=N. A. |last7=Schreier |first7=E. J. |last8=Covone |first8=G. |title=The true nature of CSL-1 |year=2006}}</ref> A cosmic string would produce a similar duplicate image of fluctuations in the [[cosmic microwave background]], which it was thought might have been detectable by the [[Planck Surveyor]] mission.<ref>{{cite journal |arxiv=0708.1162 |bibcode=2008PhRvD..78d3535F |doi=10.1103/PhysRevD.78.043535 |title=Small-angle CMB temperature anisotropies induced by cosmic strings |year=2008 |last1=Fraisse |first1=Aurélien |last2=Ringeval |first2=Christophe |last3=Spergel |first3=David |last4=Bouchet |first4=François |journal=Physical Review D |volume=78 |issue=4 |pages=43535 |s2cid=119145024 }}</ref> However, a 2013 analysis of data from the Planck mission failed to find any evidence of cosmic strings.<ref name="planck_strings">{{Cite journal|arxiv=1303.5085 |author1=Planck Collaboration |last2=Ade |first2=P. A. R. |last3=Aghanim |first3=N. |last4=Armitage-Caplan |first4=C. |last5=Arnaud |first5=M. |last6=Ashdown |first6=M. |last7=Atrio-Barandela |first7=F. |last8=Aumont |first8=J. |last9=Baccigalupi |first9=C. |title=Planck 2013 results. XXV. Searches for cosmic strings and other topological defects |journal=Astronomy & Astrophysics |volume=571 |pages=A25 |year=2013|last10= Banday |first10=A. J. |last11= Barreiro |first11=R. B. |last12= Bartlett |first12=J. G. |last13= Bartolo |first13=N. |last14= Battaner |first14=E. |last15= Battye |first15=R. |last16= Benabed |first16=K. |last17= Benoît |first17=A. |last18= Benoit-Lévy |first18=A. |last19= Bernard |first19=J. -P. |last20= Bersanelli |first20=M. |last21= Bielewicz |first21=P. |last22= Bobin |first22=J. |last23= Bock |first23=J. J. |last24= Bonaldi |first24=A. |last25= Bonavera |first25=L. |last26= Bond |first26=J. R. |last27= Borrill |first27=J. |last28= Bouchet |first28=F. R. |last29= Bridges |first29=M. |last30= Bucher |first30=M. |display-authors=29 |doi=10.1051/0004-6361/201321621 |bibcode=2014A&A...571A..25P|s2cid=15347782 }}</ref>

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>

Currently the most sensitive bounds on cosmic string parameters come from the non-detection of gravitational waves by [[Pulsar timing array]] data.<ref>{{Cite journal|arxiv=1508.03024 |title=The NANOGrav Nine-year Data Set: Limits on the Isotropic Stochastic Gravitational Wave Background |journal=The Astrophysical Journal |volume=821 |issue=1 |pages=13 |year=2015|last1=Arzoumanian |first1=Zaven |last2=Brazier |first2=Adam |last3=Burke-Spolaor |first3=Sarah |last4=Chamberlin |first4=Sydney |last5=Chatterjee |first5=Shami |last6=Christy |first6=Brian |last7=Cordes |first7=Jim |last8=Cornish |first8=Neil |last9=Demorest |first9=Paul |last10=Deng |first10=Xihao |last11=Dolch |first11=Tim |last12=Ellis |first12=Justin |last13=Ferdman |first13=Rob |last14=Fonseca |first14=Emmanuel |last15=Garver-Daniels |first15=Nate |last16=Jenet |first16=Fredrick |last17=Jones |first17=Glenn |last18=Kaspi |first18=Vicky |last19=Koop |first19=Michael |last20=Lam |first20=Michael |last21=Lazio |first21=Joseph |last22=Levin |first22=Lina |last23=Lommen |first23=Andrea |last24=Lorimer |first24=Duncan |last25=Luo |first25=Jin |last26=Lynch |first26=Ryan |last27=Madison |first27=Dustin |last28=McLaughlin |first28=Maura |last29=McWilliams |first29=Sean |last30=Mingarelli |first30=Chiara |display-authors=29 |doi=10.3847/0004-637X/821/1/13 |bibcode = 2016ApJ...821...13A |s2cid=34191834 }}</ref> The earthbound [[LIGO|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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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.

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.

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.

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== 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|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|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|issn=0035-8711|arxiv=1801.04140|bibcode=2018MNRAS.478.1132V|s2cid=53330913}}</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. |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}}

* {{cite arXiv |eprint=astro-ph/0503120 |last1=Lo |first1=Amy S. |last2=Wright |first2=Edward L. |title=Signatures of Cosmic Strings in the Cosmic Microwave Background |year=2005}}

* {{cite journal |arxiv=astro-ph/0506400 |bibcode=2006ApJ...636L...5S|doi=10.1086/499429 |title=Further Spectroscopic Observations of the CSL 1 Object |year=2006 |last1=Sazhin |first1=M. |last2=Capaccioli |first2=M. |last3=Longo |first3=G. |last4=Paolillo |first4=M. |last5=Khovanskaya |first5=O. |journal=The Astrophysical Journal |volume=636 |issue=1|pages=L5–L8|s2cid=10176938}}

* {{cite journal |arxiv=astro-ph/0603838 |bibcode=2006PhRvD..73h7302A|doi=10.1103/PhysRevD.73.087302 |title=Hubble imaging excludes cosmic string lens |year=2006 |last1=Agol |first1=Eric |last2=Hogan |first2=Craig |last3=Plotkin |first3=Richard |journal=Physical Review D |volume=73 |issue=8|pages=87302 |s2cid=119450257}}

* [[Kip Thorne|Dr. Kip Thorne]], ITP & Caltech. ''Spacetime Warps and the Quantum: A Glimpse of the Future.'' [http://online.kitp.ucsb.edu/online/plecture/thorne/ Lecture slides and audio]

* [http://xstructure.inr.ac.ru/x-bin/theme3.py?level=1&index1=443810 Cosmic strings and superstrings on arxiv.org]