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 π_{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 *η* ~ 10^{16} 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__:
∇^{2}*φ* =
4π*G* (*ρ* + *p*_{1}
+ *p*_{2} + *p*_{3});
For a straight string along the 1-axis, *p*_{1}
= −*ρ*, *p*_{2}
= *p*_{3} = 0, so
*φ* satisfies the Laplace equation; The infinite-string
metric is d*s*^{2}
= −d*t*^{2}
+ d*z*^{2}
+ d*r*^{2}
+ (1−4*Gμ*) *r*^{2}
d*θ*^{2} (locally flat).

* __Properties__:
If *η* = 10^{16} GeV,
their thickness is 10 cm, their density 10^{22} 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 *A*_{θ} = 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 PRD(15)-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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