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*G**μ*) *r*^{2}
d*θ*^{2} (locally flat).

* __Properties__: If *η* =
10^{16} GeV,
their thickness is 10 cm, their density 10^{22} g/cm
(*G**μ* = 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*/*G**μ*;
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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