Cosmic Strings  

In General > s.a. cosmic-string phenomenology; 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 π1(G/H) = 0; Originally considered as unrelated to fundamental strings; They arise in GUTs, associated with some spontaneous symmetry breaking, around an energy scale η ~ 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; Paczyński; 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: ∇2φ = 4πG (ρ + p1 + p2 + p3); For a straight string along the 1-axis, p1 = –ρ, p2 = p3 = 0, so φ satisfies the Laplace equation; The infinite-string metric is ds2 = –dt2 + dz2 + dr2 + (1–4Gμ) r2 dθ2 (locally flat).
* Properties: If η = 1016 GeV, their thickness is 10 cm, their density 1022 g/cm (Gμ = 10– 6); Their shape is that of a random walk with correlation length ξ < t (from causality) and their distance from each other ξ.
* 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 = Gμt.
* Action and dynamics: One can use the Nambu-Goto action, in the thin-string approximation; A finite action is obtained coupling φ ∈ \(\mathbb C\) to an electromagnetic field with Aθ = 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 τ = L/Gμ; For L \(\ll\) horizon length, expansion is unimportant; The evolution of patterns is self-similar.

Superconducting Cosmic Strings > s.a. gamma-ray astronomy [GRBs].
* 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.
@ 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]; Ferrer & Vachaspati PRL(05)ap [galactic 511-KeV photons]; Vachaspati PRL(08)-a0802 [cosmic sparks?]; Miyamoto & Nakayama JCAP(13)-a1212 [cosmological and astrophysical constraints].

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-proc; Gangui ap/01-ln.
@ General articles: Kibble JPA(76); Xanthopoulos PLB(86), PRD(87); Garfinkle & Will PRD(87); Turok ed; Hodges PRD(89); Carter PLB(90)ht/07.
@ Reviews: Gibbons et al ed-90 [formation and evolution]; Davis & Brandenberger ed-95; Rajantie IJMPA(02); Anderson 03 [mathematical]; Kibble ap/04-conf [renewed interest]; Vilenkin in(06)ht/05; Sakellariadou AdP(06)ht/05-conf, LNP(07)ht/06, NPPS(09)-a0902; Copeland & Kibble PRS(10)-a0911; Vachaspati et al Schol(15)-a1506.
@ Networks: Vachaspati & Vilenkin PRD(87); Hindmarsh hp/98-talk [particle production]; Magueijo et al PRD(99)ap [statistics]; Sakellariadou JCAP(05) [characteristic scale]; 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]; Lorenz et al JCAP(10)-a1006 [number density distribution of cosmic-string loops]; Blanco-Pillado et al PRD(11)-a1101 [large numerical simulations]; Martins JPCS(14)-a1310 [scaling properties]; Blanco-Pillado et al PRD(14) [loops, mass and speed spectrum]; Hindmarsh et al PRD(14)-a1409 [improving simulations]; Avgoustidis et al PRD(15)-a1411 [dynamics of Y-junctions]; > s.a. gravitational-wave background.
@ Small-scale structure: Siemens et al PRD(02) [smallest scales]; Martins & Shellard PRD(06)ap/05; Polchinski & Rocha PRD(06)hp/06; Polchinski PTRS(08)-a0803-conf; Martins et al PRD(14)-a1405 [analytic model for wiggly strings].
@ 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]; Copi & Vachaspati PRD(11)-a1010 [simple stable loop configurations]; Blanco-Pillado et al a1508 [loop shapes].
@ 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 spacetime]; 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 cosmological constant]; Lee et al PRD(11)-a1108 [4D string or brane-like solutions with a cosmological constant]; Kunze & Sakellariadou JCAP(11)-a1106 [anisotropic backgrounds].
@ In other theories: Aldrovandi PRD(07)-a0706 [Einstein-Yang-Mills-Higgs theory]; Long et al JCAP(14)-a1405 [hidden sector, "dark strings"]; > s.a. Mimetic Gravity.
@ And quantum field theory: Linet PRD(87); Iellici CQG(97) [scalar field]; > s.a. quantum field theory in curved backgrounds.
@ Related topics: Raychaudhuri PRD(90) [and general relativity]; Bezerra & Letelier CQG(91) [loop variables]; Anandan PRD(96)gq/95 [geometric phase]; Cho & Vilenkin PRD(99)ht/98, PRD(99)gq/98 [without a vacuum]; Janca a0705 [and weak energy condition violation]; > s.a. hořava-lifshitz gravity.

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