The form of cosmic string cusps

J. J. Blanco-Pillado; Ken D. Olum

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The form of cosmic string cusps

J. J. Blanco-Pillado, Ken D. Olum

General Relativity and Quantum Cosmology · Submitted 1 Oct 1998

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

The authors' main claim Since $r << L $ for cosmological strings, the radiation is strongly suppressed and could not be observed.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.53 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.75 · compares with prior results 0.93 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We classify the possible shapes of cosmic string cusps and how they transform under Lorentz boosts. A generic cusp can be brought into a form in which the motion of the cusp tip lies in the plane of the cusp. The cusp whose motion is perpendicular to this plane, considered by some authors, is a special case and not the generic situation. We redo the calculation of the energy in the region where the string overlaps itself near a cusp, which is the maximum energy that can be released in radiation. We take into account the motion of a generic cusp and the resulting Lorentz contraction of the string core. The result is that the energy scales as $\sqrt {rL}$ instead of the usual value of $r^{1/3} L^{2/3}$, where $r$ is the string radius and $L$ and is the typical length scale of the string. Since $r << L $ for cosmological strings, the radiation is strongly suppressed and could not be observed.

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 classify the possible shapes of cosmic string cusps and how they transform under Lorentz boosts.	contribution 1.00	0.90	0.08	asserted 0.93
s1	A generic cusp can be brought into a form in which the motion of the cusp tip lies in the plane of the cusp.	result 0.78	0.74	0.10	asserted 0.88
s2	The cusp whose motion is perpendicular to this plane, considered by some authors, is a special case and not the generic situation.	result 0.73	0.26	0.09	asserted 1.00
s3	We redo the calculation of the energy in the region where the string overlaps itself near a cusp, which is the maximum energy that can be released in radiation.	contribution 0.91	0.94	0.06	asserted 0.98
s4	We take into account the motion of a generic cusp and the resulting Lorentz contraction of the string core.	method 0.82	0.83	0.04	asserted 0.90
s5	The result is that the energy scales as $\sqrt {rL}$ instead of the usual value of $r^{1/3} L^{2/3}$, where $r$ is the string radius and $L$ and is the typical length scale of the string.	result 1.00	0.93	0.67	asserted 1.00
s6	Since $r << L $ for cosmological strings, the radiation is strongly suppressed and could not be observed.	interpretation 0.97	0.72	0.45	hedged possibility 0.97

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

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The paper

Original abstract

We classify the possible shapes of cosmic string cusps and how they transform under Lorentz boosts. A generic cusp can be brought into a form in which the motion of the cusp tip lies in the plane of the cusp. The cusp whose motion is perpendicular to this plane, considered by some authors, is a special case and not the generic situation. We redo the calculation of the energy in the region where the string overlaps itself near a cusp, which is the maximum energy that can be released in radiation. We take into account the motion of a generic cusp and the resulting Lorentz contraction of the string core. The result is that the energy scales as $\sqrt {rL}$ instead of the usual value of $r^{1/3} L^{2/3}$, where $r$ is the string radius and $L$ and is the typical length scale of the string. Since $r << L $ for cosmological strings, the radiation is strongly suppressed and could not be observed.

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References

Forward citations

Cited by 11 Pith papers

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

Cosmic F- and D-strings
hep-th 2003-12 accept novelty 8.0 of 10

Long-lived cosmic strings built from bound fundamental and Dirichlet strings can exist in brane-inflation models, with tensions near 10^-10 to 10^-9 in G-mu, inside the reach of planned gravitational-wave detectors.
Diamonds in the sky: the shape of gravitational waves from cosmic string cusps
gr-qc 2026-10 conditional novelty 6.0 of 10

Cosmic string cusp gravitational wave beams are diamond-shaped, not conical, with peak emission offset from the cusp direction; averaged loop power is barely affected.
Beyond the Standard Models with Cosmic Strings
hep-ph 2019-12 conditional novelty 6.0 of 10

Solving the velocity-dependent one-scale equations through cosmological transitions shifts the cosmic-string gravitational-wave turning point to lower frequency by a factor of about 22, letting future interferometers ...
The number of cosmic string loops
astro-ph.CO 2013-09 conditional novelty 6.0 of 10

The paper derives the mass and velocity distribution of cosmic string loops from simulations and converts it into a pulsar-timing bound on the string tension of Gμ ≤ 2.8×10⁻⁹.
Abelian Higgs Cosmic Strings: Small Scale Structure and Loops
hep-th 2008-12 conditional novelty 6.0 of 10

Abelian Higgs string simulations confirm the predicted tangent-vector power law but find loop densities about two orders of magnitude too low for loops to carry away the network's energy, pointing to direct massive ra...

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Cogenesis of baryon and lepton number asymmetries matching the EMPRESS Data
hep-ph 2025-09 conditional novelty 5.0 of 10

A U(1)_{B-L} flaton decay chain can produce both a large positive electron-neutrino asymmetry and the observed baryon asymmetry, with values matching EMPRESS and BBN for a symmetry-breaking scale around 10^10 GeV.
Monopoles, Strings, Walls and Gravitational waves
hep-ph 2026-07 conditional novelty 4.0 of 10

Breaking SU(2) flavor gauge symmetry stepwise to nothing leaves monopoles, strings, and walls; collapsing walls can form composite strings whose gravitational-wave spectra fit PTA data and lie within reach of LVK and ...
Magnetic monopoles and high frequency gravitational waves from quasi-stable strings
hep-ph 2026-03 conditional novelty 4.0 of 10

SO(10) breaking through flipped SU(5) or Pati-Salam subgroups can produce GUT monopoles from merging monopole-antimonopole pairs, while the intervening quasi-stable strings emit gravitational waves from Hz to kHz.
C-parity, magnetic monopoles and higher frequency gravitational waves
hep-ph 2025-02 conditional novelty 4.0 of 10

The C-string-wall network from SO(10) breaking with unbroken C-parity produces a gravitational wave background peaking between 100 Hz and 100 kHz for intermediate breaking scales around 10^10 to 10^12 GeV.
Signals of Inflationary Models with Cosmic Strings
astro-ph.CO 2011-06 accept novelty 3.0 of 10

A review of the observational signatures of cosmic strings produced at the end of inflation, concluding that CMB data already bound the string tension G-mu below roughly 10^-6, while the loop population and hence the ...
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

22 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 · 29 sentences without a confident label

Uses its data or values 2 papers

If we were to use to value of $l_c$ given by [ref] , which takes into account effects which were not included in the initial analysis of [ref] , and is

Cosmic Ray Positrons from Cosmic Strings · Conclusions and Discussion · 0.88
The length of the overlapping segment has been estimated to be $√(r l)$ [ref] where $r ≃μ^-1/2$ is the string core size and $l$ is the loop length.

Beyond the Standard Models with Cosmic Strings · Beyond the Nambu-Goto approximation · 0.91

Cites it as support 1 paper

Therefore, if particle emission from cusps should indeed provide an efficient energy loss channel for string loops at early times, in line with the estimates in Refs. [ref] , we are able to draw two conclusions: (i) $T_cusp ≪T_fric$ implies that we must not identify the initial time $t_ini$ that enters the computation of the GWB spectrum with the end of the friction regime.

Gravitational waves from low-scale cosmic strings · Initial loop length · 0.98

Cites it as background 6 papers

These equations can develop three classes of perturbations [ref] , depending on the parameter which is subject to change: shocks (the current), kinks (the curvature), cusps (the spatial geometry).

Kink in superconducting cosmic string: exact solution · Introduction · 0.83
A defining feature of these singularities is that the string momentarily reaches the speed of light and develops a characteristic geometric structure, commonly referred to as a cusp [ref] .

Cuspidal Singularities in Collapsing Domain Walls · Worldvolume Singularity Formation in the Nambu-Goto limit · 0.86
4) Particle radiation from cusps: Besides kink–kink collisions, particle emission can also originate from cusps that form and propagate on string loops [ref] .

Gravitational waves from low-scale cosmic strings · Initial loop length · 0.81

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