Evolution of cosmic string configurations

Daren Austin; E.J. Copeland; T.W.B. Kibble

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Evolution of cosmic string configurations

Daren Austin, E.J. Copeland, T.W.B. Kibble

High Energy Physics - Phenomenology · Submitted 22 Jul 1993

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim With plausible assumptions about the unknown parameters in the model, we confirm the conclusions of our previous study, that if gravitational radiation and small-scale structure effects are neglected, the two dominant length scales both scale in proportion to the horizon size.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.58 · human participants 0.01 · controlled comparison 0.16 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.94 · mentions code or data availability 0.02.

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We extend and develop our previous work on the evolution of a network of cosmic strings. The new treatment is based on an analysis of the probability distribution of the end-to-end distance of a randomly chosen segment of left-moving string of given length. The description involves three distinct length scales: $\xi$, related to the overall string density, $\bar\xi$, the persistence length along the string, and $\zeta$, describing the small-scale structure, which is an important feature of the numerical simulations that have been done of this problem. An evolution equation is derived describing how the distribution develops in time due to the combined effects of the universal expansion, of intercommuting and loop formation, and of gravitational radiation. With plausible assumptions about the unknown parameters in the model, we confirm the conclusions of our previous study, that if gravitational radiation and small-scale structure effects are neglected, the two dominant length scales both scale in proportion to the horizon size. When the extra effects are included, we find that while $\xi$ and $\bar\xi$ grow, $\zeta$ initially does not. Eventually, however, it does appear to scale, at a much lower level, due to the effects of gravitational back-reaction.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We extend and develop our previous work on the evolution of a network of cosmic strings.	contribution 0.61	0.80	0.02	asserted 0.86
s1	The new treatment is based on an analysis of the probability distribution of the end-to-end distance of a randomly chosen segment of left-moving string of given length.	method 0.85	0.83	0.03	asserted 0.99
s2	The description involves three distinct length scales: $\xi$, related to the overall string density, $\bar\xi$, the persistence length along the string, and $\zeta$, describing the small-scale structure, which is an important feature of the numerical simulations that have been done of this problem.	method 0.84	0.24	0.04	asserted 0.99
s3	An evolution equation is derived describing how the distribution develops in time due to the combined effects of the universal expansion, of intercommuting and loop formation, and of gravitational radiation.	method 0.50	0.94	0.08	asserted 1.00
s4	With plausible assumptions about the unknown parameters in the model, we confirm the conclusions of our previous study, that if gravitational radiation and small-scale structure effects are neglected, the two dominant length scales both scale in proportion to the horizon size.	result 0.98	0.75	0.28	asserted 0.85
s5	When the extra effects are included, we find that while $\xi$ and $\bar\xi$ grow, $\zeta$ initially does not.	result 1.00	0.95	0.19	asserted 1.00
s6	Eventually, however, it does appear to scale, at a much lower level, due to the effects of gravitational back-reaction.	result 1.00	0.89	0.16	hedged possibility 0.76

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.96.

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The paper

Original abstract

We extend and develop our previous work on the evolution of a network of cosmic strings. The new treatment is based on an analysis of the probability distribution of the end-to-end distance of a randomly chosen segment of left-moving string of given length. The description involves three distinct length scales: $\xi$, related to the overall string density, $\bar\xi$, the persistence length along the string, and $\zeta$, describing the small-scale structure, which is an important feature of the numerical simulations that have been done of this problem. An evolution equation is derived describing how the distribution develops in time due to the combined effects of the universal expansion, of intercommuting and loop formation, and of gravitational radiation. With plausible assumptions about the unknown parameters in the model, we confirm the conclusions of our previous study, that if gravitational radiation and small-scale structure effects are neglected, the two dominant length scales both scale in proportion to the horizon size. When the extra effects are included, we find that while $\xi$ and $\bar\xi$ grow, $\zeta$ initially does not. Eventually, however, it does appear to scale, at a much lower level, due to the effects of gravitational back-reaction.

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References

Forward citations

Cited by 9 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Cosmic superstrings in large volume compactifications: PTAs, LISA and time-varying tension
astro-ph.CO 2025-04 conditional novelty 7.0 of 10

Cosmic superstrings with a time-varying tension in large-volume string compactifications generically predict a LISA-band spectral drop and a high-frequency f^4 boost, encoding the mass and decay of the volume modulus.
Cosmological evolution of cosmic string loops
astro-ph 2005-11 conditional novelty 7.0 of 10

Cosmic string loops in an expanding universe reach a self-similar scaling distribution down to a few thousandths of the horizon size, without gravitational backreaction.
Gravitational Wave Background from Metastable Current-Carrying Cosmic Strings
astro-ph.CO 2026-10 conditional novelty 6.0 of 10

Current-carrying metastable cosmic strings can mimic the pulsar timing array signal, but the same parameter region is in tension with the LVK bound unless an extra high-frequency suppression mechanism is added.
Probing the gravitational wave background from cosmic strings with LISA
astro-ph.CO 2019-09 conditional novelty 6.0 of 10

LISA is projected to probe cosmic string tensions G mu down to about 1e-17 and to measure spectral features from early-universe physics.
Backreaction on an infinite helical cosmic string
astro-ph.CO 2019-08 accept novelty 6.0 of 10

For a small-amplitude helical breather cosmic string, gravitational backreaction produces energy loss matching Sakellariadou's power and a rotation of the generators that advances the oscillation phase.

Show 4 more citing papers

Collisions of Cosmic F- and D-strings
hep-th 2004-05 accept novelty 6.0 of 10

Perturbative string calculations give reconnection probabilities for all pairs of cosmic F-, D-, and (p,q) strings, generally below one, so stringy cosmic strings can in principle be distinguished from gauge-theory solitons.
Cosmic string loop distribution on all length scales and at any redshift
astro-ph.CO 2010-06 conditional novelty 5.0 of 10

Cosmic string loops settle into a universal scaling distribution on all length scales, with a scale-independent plateau below the gravitational backreaction cutoff, and today's loop density is bounded in terms of the ...
The nanohertz stochastic gravitational wave background from cosmic string loops and the abundant high redshift massive galaxies
astro-ph.HE 2023-06 conditional novelty 4.0 of 10

A two-parameter fit of cosmic string loop models to the NANOGrav 15-year spectrum succeeds, but the same parameters underpredict the JWST high-redshift stellar mass density by orders of magnitude, so no single loop po...
Introduction to Cosmic F- and D-Strings
hep-th 2004-12 accept novelty 3.0 of 10

Cosmic-scale F- and D-strings can arise naturally when branes annihilate at the end of warped brane inflation, and their gravitational-wave cusps could be detectable by LIGO.

How the literature uses it

26 arXiv papers cite this in 38 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 25 sentences without a confident label

Contests it 1 paper

The inclusion of the time-dependence reveals that loop formation leads to a strong correction to the distribution of long-distance configurations, which was not accounted for in the earlier approach [ref] .[These same issues were faced in the pioneering work [ref] , but our framework differs.]

Analytic Approaches to the Study of Small Scale Structure on Cosmic String Networks · Preliminary considerations · contest 0.77

Uses its method or tool 1 paper

In order to track their evolution in the matter-radiation transition we make use of the velocity-one scale (VOS) model [ref] , by evolving the equations dlnξ/dη=(1+^2)dlna/dη + c̃ /2 ξ , d/dη=(1-^2)(k̃/ξ-2 dlna/dη) , where $c̃$ is a constant quantifying the energy loss rate (set to a value $0.23$ to agree with CMBACT), and

The bispectrum of matter perturbations from cosmic strings · Gaussian model for the cosmic string · 0.97

Compares with it 2 papers

This is reminiscent of the three-scale model [ref] , but actually there are two crucial differences.

Models for Small-Scale Structure on Cosmic Strings: I. Mathematical Formalism · Simple consequences · 0.93
This is reminiscent of the three-scale model [ref] , with two crucial differences.

Scaling solutions of wiggly cosmic strings · Wiggly strings · 0.91

Cites it as background 9 papers

It is well known that, modulo the subtleties discussed in the introduction, cosmic string networks reach a configuration dubbed as the scaling regime [ref] (see also [ref] for a pedagogical discussion): a self-similar configuration in which the energy density $ρ$ of the system remains a fixed fraction of the energy density of the background (which we implicitly assume is much larger than that of the strings, thus leading the expansion of the Universe).

Cosmic (super)strings with a time-varying tension · String networks with constant tension · 0.99
Analytic arguments for the scaling solution were later given by Kibble & Copeland [ref] , but confusion reigned about the situation on small scales, with some simulations finding copious production of small loops [ref] and uncertainty about the role of `kinks' and other structure on the strings [ref] .

Cosmological Lithium Solution from Discrete Gauged Baryon Minus Lepton Number · Cosmic String Evolution · 0.91
It has been known since the early days of the subject that, whenever a network of cosmic strings is formed, it will quickly reach an attractor known as the scaling regime, where the energy density of the strings constitutes a fixed fraction of the background [ref] .

Cosmic superstrings in large volume compactifications: PTAs, LISA and time-varying tension · Properties of the network · 0.98

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