Cosmic Strings  

In General > s.a. Vortex.
* Idea: Thin flux tubes of "false vacuum" for gauge and Higgs fields, that arise when a group G is broken to a subgroup H, and 1(G/H) = 0; Originally considered as unrelated to fundamental strings; They arise in GUTs, associated with some spontaneous symmetry breaking, around an energy scale 1016 GeV.
* History: 1981, First studied by Vilenkin (for uniform mass and angular momentum density), who showed they give rise to gravitational lenses; Later studied also by Gott; Paczynski; Kaiser and Stebbins; Interest in them as seeds for large-scale structure decreased, but after 2000 new possible effect were proposed, and a connection with string theory.
* Approximations: Although they present neither singularities nor hard walls, their stress-energy is often assumed for simplicity to be distributional on an infinitely long line; The metric exhibits thus a conical singularity on the string; If they are uniform, one gets that they have to rotate rigidly in order to obtain a solution of Einstein's equation.
* Gravitational field: 2 = 4G ( + p1 + p2 + p3); For a straight string along the 1-axis, p1 = –, p2 = p3 = 0, so satisfies the Laplace equation; The infinite-string metric is ds2 = –dt2 + dz2 + dr2 + (1–4G) r2 d2 (locally flat).
* Properties: If = 1016 GeV, their thickness is 10 cm, their density 1022 g/cm (G = 10– 6); Their shape is that of a random walk with correlation length < t (from causality) and their distance from each other .
* Origin: One loop forms per horizon volume per characteristic time, on the average; So, at any time there are loops of many sizes, with minimum size R = Gt.
* Action and dynamics: Nambu-Goto action, in the thin-string approximation; A finite action is obtained coupling C to an electromagnetic field with Atheta = 0 (& Unruh).
* Motion and evolution: They oscillate and form cusps, as tension tends to straighten them; Loops form even in initially infinite strings, from self-intersections, radiate gravitationally (and some electromagnetically), and shrink away in a time = L/G; For L horizon length, expansion is unimportant; The evolution of patterns is self-similar.

Superconducting Cosmic Strings
* Effects: They will develop currents when moving in a background magnetic field; This will produce an electric field and pair production, which will screen the effect of the current in the string.
@ General references: Witten NPB(85), pr(87); Mazur PRD(86); Gangui AS(00)may; Ferreira et al NPB(00)ht [scalar-tensor], ht/00/PLB [with torsion].
@ Phenomenology: Berezinsky et al PRD(01)ap/00 [and GRBs]; Ferrer & Vachaspati PRL(05)ap [galactic 511-KeV photons]; Vachaspati PRL(08)-a0802 [cosmic sparks?].

Phenomenology > s.a. [gravitating matter]; astronomical objects [B fields]; phase; inflation; sources of gravitational waves.
* Galaxy formation: Loops can act as seeds for galaxies or clusters (depending on size); Fitting observations indicates G = 10–6; Correlations are ok initially, but may not survive loop fragmentation; 2004, Cosmic strings ruled out as primary source of perturbations.
* Effects: They induce transverse motion in nearby moving objects; Doppler shifts.
* Observation: 1986, series of letters to Nature claiming they had been observed; E Turner thought he saw a double image of a quasar, showing very strong lens effect; B Paczynski interpreted it as a cosmic string or a huge black hole; Others compared the two images at other frequencies, and discovered they were not the same object.
* Bounds: Any loops still inside our galaxy are 30 pc in radius (size of the galaxy at horizon crossing time).
@ General references: Kibble PRP(80); Turok PRL(85); Vilenkin PRP(85); NS(90)oct6, p29; Brandenberger IJMPA(94) [rev], Pra(98)hp-ln; Berezinsky et al PRD(98)ap; Pogosian JCAP(04)ap [Bayesian analysis].
@ Lensing surveys: Mack et al PRD(07)ap; Chernoff & Tye a0709 [microlensing search]; Christiansen et al PRD(08); Morganson et al a0908; Thomas et al a0909 [and galaxy rotation].
@ And cmb, perturbations: Brandenberger ap/96; Pen ap/98-in [problem with cmb]; Riazuelo et al PRD(00)ap/99; Sakellariadou ap/99-in; Durrer ap/00; Gangui et al NAR(02)ap/01; Jeong & Smoot ApJ(05)ap/04 [WMAP, search]; Perivolaropoulos ap/05-in [rev]; Jeong & Smoot ApJL(07)ap/06 [technique]; Amsel et al JCAP(08)-a0709; Bevis et al PRL(08); news pw(08)jan; Hindmarsh et al a0908 [temperature bispectrum].
@ SUSY GUTs and cosmology: Jeannerot et al PRD(03)hp; Rocher & Sakellariadou hp/04/PRL, JCAP(05)hp/04.
> Related topics: see black-hole phenomenology, formation and solutions; chaotic motion; defects; lensing; light; scattering; types of metrics.

Other References > s.a. classical particles; membranes; superstring phenomenology; supersymmetric theories.
@ Intros: Vilenkin SA(87)dec; Press & Spergel PT(89)mar; Vilenkin & Shellard 94; Durrer ap/97-in; Gangui ap/01-ln; Anderson 03.
@ General articles: Xanthopoulos PLB(86), PRD(87); Garfinkle & Will PRD(87); Turok ed; Hodges PRD(89); Carter PLB(90)ht/07.
@ Reviews: Davis & Brandenberger ed-95; Anderson 02 [mathematical]; Rajantie IJMPA(02); Kibble ap/04-in [renewed interest]; Vilenkin in(06)ht/05; Sakellariadou AdP(06)ht/05-in, LNP(07)ht/06, NPPS(09)-a0902.
@ Networks: Vachaspati & Vilenkin PRD(87); Hindmarsh hp/98-in [particle production]; Magueijo et al PRD(99)ap [statistics]; Siemens et al PRD(02) [smallest scales]; Sakellariadou JCAP(05) [characteristic scale]; Martins & Shellard PRD(06)ap/05, Polchinski & Rocha PRD(06)hp/06 [small-scale structure]; Vanchurin et al PRD(06)gq/05 [loops, scaling]; Avgoustidis & Shellard PRD(06)ap/05 [reconnection probability]; Achúcarro et al PRD(07) [semilocal]; Vanchurin PRD(08)-a0712, Dubath et al PRD(08) [production of loops]; Polchinski PTRS(08)-a0803-in [small-scale behavior].
@ Metric, shape: Hiscock PRD(85) [conical]; Unruh et al PRL(89) [geodesic nature]; Clarke et al CQG(90); Özdemir GRG(01)gq/00 [wiggly, metric], IJMPA(05)gq [spinning, solutions]; Krasnikov CQG(06)gq/05 [Letelier-Gal'tsov metric].
@ Modified: Huang PRD(93)ht/04 [radiating]; Gibbons & Wells CQG(94)ht/93 [dilatonic]; Morris PRD(97) [in supergravity]; Dahia CQG(00) [angular deficit]; Lue PRD(02)ht/01 [brane world]; Dvali & Vilenkin JCAP(04)ht/03 [D- and F-strings]; > s.a. brans-dicke theory.
@ In curved spacetime: Germano et al CQG(96) [Schwarzschild]; Avelino et al PRD(03)ap/02 [cyclic universes], PRL(02)ap [contracting]; Ringeval et al JCAP(07)ap/05 [cosmological, evolution of loops]; Avgoustidis PRD(08); Bhattacharya & Lahiri PRD(08)-a0807, Brihaye & Hartmann PLB(08) [positive ].
@ And quantum field theory: Linet PRD(87); Iellici CQG(97) [scalar field]; > s.a. quantum field theory in curved backgrounds.
@ Related topics: Mazur PRL(86) [Aharonov-Bohm]; Raychaudhuri PRD(90) [and general relativity]; Bezerra & Letelier CQG(91) [loop variables]; Anandan PRD(96)gq/95 [geometric phase]; Page PRD(98)gq [capture by Kerr-Newman black hole]; Cho & Vilenkin PRD(99)ht/98, PRD(99)gq/98 [without a vacuum]; Aldrovandi PRD(07)-a0706 [in Einstein-Yang-Mills-Higgs theory]; Janca a0705 [and weak energy condition violation]; Firouzjahi et al a0907 [effects of collisions]; > s.a. horava-lifshitz gravity.

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