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Cosmic strings and other topological defects in nonscaling regimes
Cosmology and Nongalactic Astrophysics · Submitted 27 Feb 2017
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In particular we obtain new approximate analytic solutions for the behavior of the network during the radiation-to-matter and matter-to-acceleration transitions (assuming, in the latter case, the canonical $\Lambda$ cold dark matter model), and numerically calculate the relevant quantities for a range of possible dark energy models.
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The abstract, sentence by sentence
Cosmic strings are topological defects possibly formed in the early Universe, which may be observable due to their gravitational effects on the cosmic microwave background radiation or gravitational wave experiments. To this effect it is important to quantitatively ascertain the network properties, including their density, velocity or the number of strings present, at the various epochs in the observable Universe. Attempts to estimate these numbers often rely on simplistic approximations for the string parameters, such as assuming that the network is scaling. However, in cosmological models containing realistic amounts of radiation, matter and dark energy a string network is never exactly scaling. Here we use the velocity-dependent one-scale model for the evolution of a string network to better quantify how these networks evolve. In particular we obtain new approximate analytic solutions for the behavior of the network during the radiation-to-matter and matter-to-acceleration transitions (assuming, in the latter case, the canonical $\Lambda$ cold dark matter model), and numerically calculate the relevant quantities for a range of possible dark energy models.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Cosmic strings are topological defects possibly formed in the early Universe, which may be observable due to their gravitational effects on the cosmic microwave background radiation or gravitational wave experiments. | background 1.00 | 0.03 | 0.03 | hedged possibility 0.99 |
| s1 | To this effect it is important to quantitatively ascertain the network properties, including their density, velocity or the number of strings present, at the various epochs in the observable Universe. | background 0.94 | 0.05 | 0.03 | asserted 0.97 |
| s2 | Attempts to estimate these numbers often rely on simplistic approximations for the string parameters, such as assuming that the network is scaling. | background 0.89 | 0.04 | 0.03 | asserted 0.84 |
| s3 | However, in cosmological models containing realistic amounts of radiation, matter and dark energy a string network is never exactly scaling. | background 0.68 | 0.12 | 0.17 | asserted 1.00 |
| s4 | Here we use the velocity-dependent one-scale model for the evolution of a string network to better quantify how these networks evolve. | method 0.88 | 0.92 | 0.10 | asserted 0.99 |
| s5 | In particular we obtain new approximate analytic solutions for the behavior of the network during the radiation-to-matter and matter-to-acceleration transitions (assuming, in the latter case, the canonical $\Lambda$ cold dark matter model), and numerically calculate the relevant quantities for a range of possible dark energy models. | contribution 0.83 | 0.96 | 0.39 | asserted 1.00 |
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The paper
Original abstract
Cosmic strings are topological defects possibly formed in the early Universe, which may be observable due to their gravitational effects on the cosmic microwave background radiation or gravitational wave experiments. To this effect it is important to quantitatively ascertain the network properties, including their density, velocity or the number of strings present, at the various epochs in the observable Universe. Attempts to estimate these numbers often rely on simplistic approximations for the string parameters, such as assuming that the network is scaling. However, in cosmological models containing realistic amounts of radiation, matter and dark energy a string network is never exactly scaling. Here we use the velocity-dependent one-scale model for the evolution of a string network to better quantify how these networks evolve. In particular we obtain new approximate analytic solutions for the behavior of the network during the radiation-to-matter and matter-to-acceleration transitions (assuming, in the latter case, the canonical $\Lambda$ cold dark matter model), and numerically calculate the relevant quantities for a range of possible dark energy models.
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How the literature uses it
1 arXiv paper cite this in 1 sentence
What it cites · 28 sentences without a confident label
Uses the method or tool of 1 paper
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Therefore the system of equations to be numerically integrated is dlnθ/dln(1+z)= dlnH(z)/dln(1+z)-(1+v^2)-cv/2θ dv/dln(1+z)=(1-v^2)(2v-k(v)/θ) , with $H(z)$ given by the Friedmann equation (cf. Eq. [ref]) and the momentum parameter given by [ref] k(v)=2√(2)/π(1-v^2)(1+2√(2)v^3)1-8v^6/1+8v^6 .
Extending the Velocity-dependent One-scale String Evolution Model · Matter-to-acceleration transition · 0.85
Uses data or values from 3 papers
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That said, we should also point out that in integrating these equations we have kept the energy loss parameter $c$ fixed at the value $c=0.23$ obtained from calibration against numerical simulations [ref] , while for $k$ we have used the phenomenological formula given by Eq. [ref].
On the Evolution of Abelian-Higgs String Networks · Matter-to-acceleration transition · 0.99
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That said, we should also point out that in integrating these equations we have kept the energy loss parameter $c$ fixed at the value $c=0.23$ obtained from calibration against numerical simulations [ref] , while for $k$ we have used the phenomenological formula given by Eq. [ref].
Unified model for vortex-string network evolution · Matter-to-acceleration transition · 0.99
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For $Λ$CDM the number of strings in the present-day observable universe is expected to be N_0=973.0±0.6 , where the error bar has been numerically estimated from the one-sigma uncertainties coming from the relevant cosmological parameters [ref] and also takes into account the network's initial conditions (although the latter are clearly subdominant).
Planck 2015 results. XIII. Cosmological parameters · Matter-to-acceleration transition · 0.99
Cites as support 5 papers
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We expect $c_ph$ and $k_ph$ to either be constants or slowly varying parameters, and based on the results of both Goto-Nambu and field theory simulations of cosmic strings [ref] , as well as of field theory simulations of domain walls [ref] , we further expect the defect velocities to change slowly during the transition—a point already anticipated by Kibble [ref] .
Large parallel cosmic string simulations: New results on loop production · Radiation-to-matter transition · 0.97
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We expect $c_ph$ and $k_ph$ to either be constants or slowly varying parameters, and based on the results of both Goto-Nambu and field theory simulations of cosmic strings [ref] , as well as of field theory simulations of domain walls [ref] , we further expect the defect velocities to change slowly during the transition—a point already anticipated by Kibble [ref] .
Extending the velocity-dependent one-scale model for domain walls · Radiation-to-matter transition · 0.97
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We expect $c_ph$ and $k_ph$ to either be constants or slowly varying parameters, and based on the results of both Goto-Nambu and field theory simulations of cosmic strings [ref] , as well as of field theory simulations of domain walls [ref] , we further expect the defect velocities to change slowly during the transition—a point already anticipated by Kibble [ref] .
New CMB constraints for Abelian Higgs cosmic strings · Radiation-to-matter transition · 0.97
Cites as background 3 papers
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A more thorough discussion can be found in Ref. [ref] .
Physical and invariant models for defect network evolution · Invariant and physical quantities · 0.98
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For other early approaches to analytic modeling, see Refs. [ref] .
COBE vs Cosmic Strings: An Analytical Model · Introduction · 0.87
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For other early approaches to analytic modeling, see Refs. [ref] .
Evolution of cosmic string configurations · Introduction · 0.87
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