Gravitational radiation from cosmic (super)strings: bursts, stochastic background, and observational windows

Alexander Vilenkin; Thibault Damour

REVIEW

Gravitational radiation from cosmic (super)strings: bursts, stochastic background, and observational windows

Thibault Damour, Alexander Vilenkin

High Energy Physics - Theory · Submitted 22 Oct 2004 · 43 references

Pith's verdict: A careful, honest extension of the Damour-Vilenkin string-GW program to two parameters (p, ε); the scaling laws are new and useful, but the p-exponents rest on a contested network-scaling assumption the abstract hedge doesn't cover.

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CitationAlexander Vilenkin, Thibault Damour. "Gravitational radiation from cosmic (super)strings: bursts, stochastic background, and observational windows." arXiv:hep-th/0410222 (2004). https://pith.science/paper/G6VUNEGV

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The new content is the two-parameter scaling. The loop density n ~ 1/(p ΓGµ t³) comes out the same for ε≪1 and ε≫1 (Eqs. 2.14, 2.18), which is a nice observation, and the ε_eff = ε/(1+ε) trick lets them treat both regimes in one formula. The burst curve shifts up by ε^{-3/8}p^{-5/8} and right by ε^{-5/8}p^{-3/8} (Eqs. 3.13-3.14), and the stochastic background goes as Ω_g ∝ p^{-1}ε^{-1/3} (Eq. 4.9). The conversion Eq. 4.15 from pulsar-timing sensitivity to Gµ is the kind of thing people will actually use. The paper is honest about its approximations — the 0.63 discrepancy between the two derivations of Ω_g is stated, factors of order 2 are flagged, and the pulsar-timing suggestion about the Green Bank scatter is explicitly labeled 'with due reserve.' I wouldn't weight that speculation, but it isn't oversold either. The self-citation of [16,17] is fine: those are published derivations, and the new scaling analysis is independent of them. The stress-test note is right that ξ ~ t is not load-bearing; only L matters, since N_l depends on total string length, not coherence length. The soft spot is the p-scaling. Every factor of p enters through N_l ~ 1/(pα), which follows from L ~ p^{1/2}t (Eq. 2.11). The authors discuss the conflicting claims (Jones-Stoica-Tye vs Sakellariadou) at length in Section II.B and say they'll use Eqs. 2.10-2.11 'as a reasonable approximation.' That's honest, but the abstract hedge ('at least when loop sizes are not suppressed...') covers ε, not p. If L ~ pt instead, N_l ~ 1/(p²α) and Ω_g's p-exponent doubles to -2, shifting the Gµ reach of Eq. 4.15 by ~2 orders of magnitude at p = 10^{-3}. The qualitative robustness (smaller p → bigger signal) survives; the quantitative reach doesn't. The supporting simulation [38] is 'work in progress,' so this is genuinely open. Who should read it: anyone working on cosmic-string GW signatures, pulsar timing arrays, or brane-inflation string networks. The scaling laws are worth having in the toolbox. Recommendation: send it out. The derivations are clean, the approximations are stated, and the open question (the p-scaling) is exactly the kind of thing referees should press on.

Referee report

Significance

The paper is timely and directly useful: it takes the two developments most likely to invalidate the earlier LIGO/LISA forecasts for cosmic superstrings, namely suppressed reconnection and suppressed loop size, and shows with explicit scaling laws that the forecasts survive over a wide parameter range. The two independent derivations of the stochastic background amplitude (the confusion-noise integral of Eq. 4.8 and the energy-budget estimate of Eq. 4.12) agreeing to a factor of order unity is a genuine internal cross-check, not a restatement. The paper also delivers a falsifiable reach estimate, Eq. 4.15, that pulsar-timing practitioners can apply directly, and it correctly identifies the mode-number cutoff as the one place where the robustness argument can fail. The scaling exponents in Eqs. 3.13-3.14 and 4.9 are the kind of compact, quotable result that later work will build on.

Major objections (1)

[Section II.B, Eqs. (2.11)-(2.12); Eqs. (3.13)-(3.14), (4.9), (4.15); abstract sentence s5] Every factor of p in the paper's quantitative results flows through the assumed scaling L(t) ~ p^{1/2} t of Eq. (2.11), obtained by equating rho_long ~ p^{-1} mu t / t^3 with mu / L^2. The authors state this assumption openly in Section II.B and cite the conflicting claims (Jones-Stoica-Tye find L ~ xi ~ p t; Sakellariadou finds L ~ xi ~ p^{1/2} t), which is appropriate. What is not carried through is the consequence: if L ~ p t instead, the total string length in a Hubble volume is ~ p^{-2} t, the loop production rate becomes N_l ~ 1/(p^2 alpha), and the p-exponent in Eq. (4.9) doubles from -1 to -2, while the burst exponents in Eqs. (3.13)-(3.14) change correspondingly. At p = 10^{-3} this is a factor of 10^3 in Omega_g and roughly two orders of magnitude in the G mu reach quoted in Eq. (4.15). The abstract's robustness claim (s5) and the conclusions quote Eq. (4.15) as a discovery-potential number without flagging that it is conditional on a contested scaling. I would ask the authors to add one explicit sentence, in the abstract or conclusions and again near Eq. (4.15), stating what changes under L ~ p t, and to note that the wiggly-string multi-intersection caveat raised in Section II.B (which pushes the effective reconnection probability above the microscopic p) acts in the opposite direction. The qualitative conclusion that smaller p improves detectability survives either way; the quantitative reach does not, and that is the number observers will quote.

Minor objections (7)

[Section II.A, Eqs. (2.7) and (2.9)] Eq. (2.7) states alpha_st ~ Gamma G mu with an order-of-magnitude relation, while Eq. (2.9) then defines epsilon = alpha / alpha_st = alpha / (Gamma G mu) with an identity sign. It would be clearer to introduce alpha_st = Gamma G mu as a definition first and to note separately that the old estimate gave alpha ~ alpha_st.
[Section II.D and Eqs. (4.14)-(4.15)] The combination epsilon_eff = epsilon / (1 + epsilon) is introduced in Section II.D as something one 'could approximately write' to interpolate between the two regimes, but it then appears in Eqs. (4.14) and (4.15) as if it were an exact replacement. Either state that it is an interpolation used for numerical convenience, or restrict Eqs. (4.14)-(4.15) to epsilon < 1 and give the epsilon > 1 limit separately.
[Section IV, Eq. (4.8)] The justification for Eq. (4.8), replacing the integral over dz/z by the value of the integrand at z ~ 1, deserves one more sentence. The integrand of Eq. (4.1) is suppressed at small z by the step function Theta[n(f,z) - 1], so the integral is really dominated near the redshift z_c(f) at which n(f,z_c) ~ 1 rather than at z ~ 1. The agreement with the independent energy argument of Eq. (4.12) is the stronger support for the result and should be presented as such.
[Section II.B, citation [38]] Reference [38] (Vanchurin, Olum and Vilenkin) is listed as work in progress and is the sole support for the statement that xi(t) is substantially larger than L(t). Since xi does not enter the gravitational wave observables, this claim could be softened or the citation marked as preliminary in the text.
[Section IV, discussion of the 17-year pulsar data set] The suggestion that the large scatter in the Green Bank portion of the PSR 1855+09 residuals might be a transient gravitational wave burst is appropriately hedged in the text ('with due reserve', 'too early to use such data'), but it is repeated in the Conclusions without that hedge. I would keep the hedge in the Conclusions as well, so that the suggestion is not read as a result of the paper.
[Section IV, Eq. (4.15) and the parameter c] The bound c > 0.1 on the number of cusps per loop oscillation is asserted without support. Given that c enters Eq. (4.15) as c^{-3/2}, a brief justification or a reference would help the reader calibrate the quoted reach.
[Figures 1-6] The captions state the ranges of p and epsilon but do not identify which curve corresponds to which parameter value. Since the figures are the primary evidence for the robustness claim, labelling the curves (or adding a legend) would make them considerably easier to read.

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The paper

The paper claims

The paper argues that cosmic-string gravitational-wave bursts and the stochastic background remain detectable when the reconnection probability is small and loop sizes are reduced, with simple scaling laws in those two parameters.

The reading

The paper asks whether the gravitational-wave signatures of cosmic strings survive two modifications expected for cosmic superstrings: a reconnection probability $p$ well below one and a typical loop length smaller than standard by a factor $epsilon$. It redoes the burst-from-cusp and stochastic-background estimates with these parameters, keeping the string tension $Gmu$ free. The answer is that the earlier detection estimates are largely robust: lowering $p$ increases both signals, while lowering $epsilon$ changes burst amplitudes only weakly until a high-frequency cutoff appears, though the stochastic background rises as $epsilon^{-1/3}$ before that cutoff. The authors use this to argue that LIGO, LISA, and pulsar timing still have broad windows on superstring tensions, and they ask pulsar observers to check whether a large scatter in a 17-year data set could be a transient burst.

What carries the argument

The load-bearing machinery is a reparameterization of the standard string-network loop density. In the standard scenario the typical loop length is $alpha t$ with $alpha sim Gamma Gmu$, and the loop density is $n sim alpha^{-1}t^{-3}$. The paper replaces $alpha$ by $epsilonGamma Gmu$ and tracks how a low reconnection probability changes the number of long strings per Hubble volume, giving $n(t)sim (pGamma Gmu t^3)^{-1}$ for small loops and the same form in the matter era for large loops. This density change is absorbed into the cusp-event rate as $cto cepsilon/p$, or equivalently $dot Nto dot N p/epsilon$, which is what produces the scaling laws for bursts and the background. A Heaviside cutoff $Theta(1-theta_m)$ with $theta_msim(alpha f t_0)^{-1/3}(1+z)^{1/6}$ enforces that only Fourier modes with $|m|ge1$ contribute.

Extended reading notes

Core claim

The central claim is that the gravitational-wave predictions for cosmic string networks are not fragile to the two new parameters. For cusp bursts, the plot of expected amplitude versus $Gmu$ moves upward by $epsilon^{-3/8}p^{-5/8}$ and rightward by $epsilon^{-5/8}p^{-3/8}$ (Eqs. 3.13-3.14), so a smaller reconnection probability improves detectability and a smaller loop parameter mainly shifts the accessible tension range. For the stochastic background from overlapping loops, the low-frequency estimate is $Omega_g(f)propto p^{-1}epsilon^{-1/3}(Gmu)^{2/3}(f t_0)^{-1/3}$ in the regime where the loops are large enough to radiate into the observing band (Eqs. 4.9, 4.14). The important exception is a step-function cutoff when $alpha f t_0<1$, which can remove the signal from pulsar timing, and later from LIGO or LISA, if $epsilon$ is extremely small.

Load-bearing premise

The acknowledged load-bearing premise is the treatment of a low reconnection probability: the paper assumes the long-string coherence length still scales as $xi(t)sim t$ while the inter-string distance scales as $L(t)sim p^{1/2}t$, and every $p$-dependent result flows through that choice; the authors note conflicting claims in the literature and cite only preliminary simulations.

Editorial extensions

If this is right

A smaller reconnection probability $p<1$ raises both the cusp-burst amplitude and the stochastic background at fixed $Gmu$, so superstring networks can be easier to detect than ordinary strings.
For $epsilon<1$, burst detectability by LIGO and LISA is largely preserved until the mode cutoff becomes important, roughly when $epsilonlesssim10^{-11}$ for LIGO or $epsilonlesssim10^{-7}$ for LISA at $Gmusim10^{-10}$.
The existing pulsar-timing limit $Omega_g h^2<6times10^{-8}$ implies $c^{3/2}Gmulesssim10^{-7}$, while a future pulsar-timing-array sensitivity of $Omega_g h^2sim2times10^{-9}$ could probe $Gmusim3.6times10^{-10}c^{-3/2}p^{3/2}epsilon^{1/2}$.
Very small $epsilon$ can cut off the stochastic signal in the pulsar band when $alpha f t_0<1$, so pulsar timing may lose sensitivity to the smallest tensions even as higher-frequency detectors retain it.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If brane inflation produces superstrings with $p$ and $epsilon$ far from one, the amplitude scalings and the low-frequency cutoff give a way to distinguish them from ordinary field-theory strings using combined LIGO, LISA, and pulsar-timing data.
Measuring both a burst amplitude and a stochastic-background level could in principle break the degeneracy among $Gmu$, $p$, $epsilon$, and the cusp number $c$, because the two observables scale differently with these parameters.
A targeted time-domain search for transient near-cusp events in existing pulsar residuals is a low-cost test of the authors' suggestion that the Green Bank scatter is a burst rather than a steady red-noise background.
Future network simulations that map $alpha$ and $c$ as functions of $Gmu$ and $p$ would turn the paper's scaling laws into a predictive parameter space rather than a family of allowed extrapolations.

Original abstract

The gravitational wave (GW) signals emitted by a network of cosmic strings are reexamined in view of the possible formation of a network of cosmic superstrings at the end of brane inflation. The reconnection probability $p$ of intersecting fundamental or Dirichlet strings might be much smaller than 1, and the properties of the resulting string network may differ significantly from those of ordinary strings (which have $p=1$). In addition, it has been recently suggested that the typical length of newly formed loops may differ by a factor $\epsilon \ll 1$ from its standard estimate. Here, we analyze the effects of the two parameters $p$ and $\epsilon$ on the GW signatures of strings. We consider both the GW bursts emitted from cusps of oscillating string loops, which have been suggested as candidate sources for the LIGO/VIRGO and LISA interferometers, and the stochastic GW background, which may be detectable by pulsar timing observations. In both cases we find that previously obtained results are \textit{quite robust}, at least when the loop sizes are not suppressed by many orders of magnitude relative to the standard scenario. We urge pulsar observers to reanalyze a recently obtained 17-year combined data set to see whether the large scatter exhibited by a fraction of the data might be due to a transient GW burst activity of some sort, e.g. to a near cusp event.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,856 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.84 · human participants 0.02 · controlled comparison 0.28 · randomized assignment 0.01 · states quantitative result 0.21 · compares with prior results 0.92 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The gravitational wave (GW) signals emitted by a network of cosmic strings are reexamined in view of the possible formation of a network of cosmic superstrings at the end of brane inflation. The reconnection probability $p$ of intersecting fundamental or Dirichlet strings might be much smaller than 1, and the properties of the resulting string network may differ significantly from those of ordinary strings (which have $p=1$). In addition, it has been recently suggested that the typical length of newly formed loops may differ by a factor $\epsilon \ll 1$ from its standard estimate. Here, we analyze the effects of the two parameters $p$ and $\epsilon$ on the GW signatures of strings. We consider both the GW bursts emitted from cusps of oscillating string loops, which have been suggested as candidate sources for the LIGO/VIRGO and LISA interferometers, and the stochastic GW background, which may be detectable by pulsar timing observations. In both cases we find that previously obtained results are \textit{quite robust}, at least when the loop sizes are not suppressed by many orders of magnitude relative to the standard scenario. We urge pulsar observers to reanalyze a recently obtained 17-year combined data set to see whether the large scatter exhibited by a fraction of the data might be due to a transient GW burst activity of some sort, e.g. to a near cusp event.

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	The gravitational wave (GW) signals emitted by a network of cosmic strings are reexamined in view of the possible formation of a network of cosmic superstrings at the end of brane inflation.	background 0.57	0.38	0.04	hedged possibility 0.52
s1	The reconnection probability $p$ of intersecting fundamental or Dirichlet strings might be much smaller than 1, and the properties of the resulting string network may differ significantly from those of ordinary strings (which have $p=1$).	background 0.99	0.05	0.03	hedged possibility 0.55
s2	In addition, it has been recently suggested that the typical length of newly formed loops may differ by a factor $\epsilon \ll 1$ from its standard estimate.	background 0.98	0.04	0.02	hedged possibility 0.94
s3	Here, we analyze the effects of the two parameters $p$ and $\epsilon$ on the GW signatures of strings.	contribution 0.99	0.73	0.04	asserted 0.90
s4	We consider both the GW bursts emitted from cusps of oscillating string loops, which have been suggested as candidate sources for the LIGO/VIRGO and LISA interferometers, and the stochastic GW background, which may be detectable by pulsar timing observations.	contribution 0.69	0.24	0.04	hedged possibility 0.82
s5	In both cases we find that previously obtained results are \textit{quite robust}, at least when the loop sizes are not suppressed by many orders of magnitude relative to the standard scenario.	result 0.97	0.94	0.81	asserted 0.98
s6	We urge pulsar observers to reanalyze a recently obtained 17-year combined data set to see whether the large scatter exhibited by a fraction of the data might be due to a transient GW burst activity of some sort, e.g. to a near cusp event.	future work 1.00	0.15	0.07	hedged possibility 0.64

What kind of paper the classifier reports this is: theoretical result 0.93 · evidence from proof or derivation 0.52.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

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A thorough investigation of cross-correlation estimators for stochastic gravitational-wave background searches in ground-based detector data
gr-qc 2026-06 unverdicted novelty 6.0 of 10

Reformulation of frequency-domain narrowband cross-correlation estimators for SGWB searches provides new expressions for estimators and covariances, while showing that widely used prior expressions still yield correct...
Directional Search for Persistent Gravitational Waves: Results from the First Part of LIGO-Virgo-KAGRA's Fourth Observing Run
gr-qc 2025-10 conditional novelty 6.0 of 10

An 8.3-year LIGO–Virgo–KAGRA search for persistent, direction-dependent gravitational waves finds no signal and yields the most restrictive upper limits to date on anisotropic backgrounds and targeted sources.
A Fog Over the Cosmological SGWB: Unresolved Massive Black Hole Binaries in the LISA Band
astro-ph.CO 2025-06 conditional novelty 6.0 of 10

Unresolved massive black hole binaries will create a stochastic foreground in LISA that can raise the minimum detectable amplitude of a cosmological gravitational wave background by up to a factor of about 40 near a s...
Gravitational Wave Bursts as Harbingers of Cosmic Strings Diluted by Inflation
hep-ph 2019-12 conditional novelty 6.0 of 10

A cosmic string network diluted by inflation can regrow to observable density by today, and its leading gravitational wave signal is resolvable bursts rather than a stochastic background.
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 ...
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.
Reconstructing the spectral shape of a stochastic gravitational wave background with LISA
astro-ph.CO 2019-06 conditional novelty 6.0 of 10

An adaptive binning procedure, implemented in the code SGWBinner, recovers the frequency profile of mock stochastic gravitational wave backgrounds in simulated LISA data across five benchmark signal families.
Probing non-Gaussian Stochastic Gravitational Wave Backgrounds with LISA
astro-ph.CO 2018-06 conditional novelty 6.0 of 10

The authors derive LISA's response functions to a general stochastic gravitational wave bispectrum and an optimal estimator for its signal-to-noise ratio, then survey early-universe models that could produce such non-...
Semianalytic Calculation of Gravitational Wave Spectrum Nonlinearly Induced from Primordial Curvature Perturbations
gr-qc 2018-04 accept novelty 6.0 of 10

A closed-form expression for the time integral in the second-order gravitational-wave power spectrum makes induced gravitational-wave predictions from primordial curvature perturbations fast to compute.
Stochastic gravitational wave background from smoothed cosmic string loops
astro-ph.CO 2017-09 conditional novelty 6.0 of 10

A full pipeline from simulated cosmic string loops through smoothing, per-loop gravitational wave spectra, and standard-model cosmology yields the present-day stochastic background as a function of string tension.
CMB constraints on cosmic strings and superstrings
astro-ph.CO 2016-03 conditional novelty 6.0 of 10

Joint MCMC fits to Planck 2015 data give Gμ < 1.1e-7 for cosmic strings and Gμ_F < 2.8e-8 for superstrings, marginalizing over network and string-theory parameters.
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.
Searching For Anisotropic Gravitational-wave Backgrounds Using Pulsar Timing Arrays
gr-qc 2013-06 conditional novelty 6.0 of 10

A Bayesian pulsar-timing pipeline recovers injected dipole and quadrupole anisotropies in a simulated gravitational-wave background and shows that isotropy becomes a poor model at high signal-to-noise.
Cosmic string gravitational wave backgrounds at LISA: II. Reconstruction of conventional signals over astrophysical foregrounds
astro-ph.CO 2026-07 conditional novelty 5.0 of 10

When realistic astrophysical foregrounds are included, LISA can reconstruct the cosmic-string tension to 10% precision only for Gμ ≳ 10^{-11}, 10^5 times larger than foreground-free forecasts.
Cosmic string gravitational wave backgrounds at LISA: I. Signal survey, template reconstruction, and model comparison
astro-ph.CO 2025-08 unverdicted novelty 5.0 of 10

As provided, the manuscript body (random lasing) does not correspond to the abstract (cosmic string gravitational wave backgrounds at LISA), leaving the abstract's quantitative claims unsupported by any accessible text.
Primordial Gravitational Waves from Phase Transitions during Reheating
astro-ph.CO 2025-06 conditional novelty 5.0 of 10

Phase transitions happening during reheating can produce gravitational-wave signals that are delayed, prolonged, and shifted in amplitude and frequency by orders of magnitude compared with standard cosmology.
Searching beyond the fiducial stochastic gravitational wave background in pulsar timing array data using likelihood reweighting
gr-qc 2025-04 conditional novelty 5.0 of 10

A two-stage likelihood reweighting method recovers the parameters and Bayes factor of an added sinusoid signal in simulated pulsar timing data, matching full Bayesian analyses while claiming about a tenfold speedup.
Cosmological Interpretation for the Stochastic Signal in Pulsar Timing Arrays
astro-ph.CO 2023-07 conditional novelty 5.0 of 10

Combining NANOGrav, PPTA and EPTA data, first-order phase transitions and cosmic strings fit the nanohertz gravitational-wave signal about as well as supermassive black hole binaries, while domain walls are disfavored...
Cosmological Background Interpretation of Pulsar Timing Array Data
astro-ph.CO 2023-07 conditional novelty 5.0 of 10

Combined NANOGrav and EPTA pulsar timing data prefer scalar-induced and superstring gravitational-wave backgrounds over a simple supermassive-black-hole-binary power law, and constrain primordial non-Gaussianity to |f...
Gravitational Waves from Global Cosmic Strings and Cosmic Archaeology
hep-ph 2021-06 conditional novelty 5.0 of 10

A calibrated analytic model of global cosmic string networks predicts a gravitational wave spectrum that falls as a log-cubed power law, and whose shape maps observed frequencies onto cosmic temperatures as high as 10^8 GeV.
Comparison of cosmic string and superstring models to NANOGrav 12.5-year results
astro-ph.CO 2021-02 conditional novelty 5.0 of 10

Across four models of the gravitational-wave spectrum of cosmic string loops, the string tension that fits the NANOGrav 12.5-year common-spectrum signal stays in the range Gµ of roughly 10^-10.0 to 10^-10.7.
The POEMMA (Probe of Extreme Multi-Messenger Astrophysics) Observatory
astro-ph.IM 2020-12 conditional novelty 5.0 of 10

A NASA Probe-class concept study describes a two-satellite observatory that would measure ultra-high-energy cosmic rays over the full sky and hunt tau neutrinos above 20 PeV by imaging their upward air showers from orbit.
Gravitational waves and proton decay: complementary windows into GUTs
hep-ph 2020-05 conditional novelty 5.0 of 10

Proton-decay and cosmic-string gravitational-wave bounds, taken together, favour SO(10) breaking through SU(5)xU(1) or Pati-Salam and disfavour flipped SU(5)xU(1) or plain SU(5), conditional on the NANOGrav signal bei...
Constraints on cosmic strings using data from the first Advanced LIGO observing run
gr-qc 2017-12 accept novelty 5.0 of 10

No gravitational-wave bursts from cosmic string cusps or kinks appear in Advanced LIGO O1 data, and the resulting upper limits, combined with stochastic, pulsar-timing, CMB and BBN bounds, exclude large parts of the p...
Digging deeper: Observing primordial gravitational waves below the binary black hole produced stochastic background
astro-ph.CO 2016-11 conditional novelty 5.0 of 10

With five third-generation detectors, the binary black hole confusion background can be pushed below 10^-13, low enough for the primordial gravitational-wave background to become the limiting signal, provided detected...
Science with the space-based interferometer LISA. IV: Probing inflation with gravitational waves
astro-ph.CO 2016-10 conditional novelty 5.0 of 10

LISA's projected sensitivity curves are mapped onto four inflationary gravitational-wave production mechanisms, showing that each can produce a signal above the irreducible vacuum tensor background for some range of m...
Stochastic Gravitational Wave Background generated by Cosmic String Networks: Velocity-Dependent One-Scale model versus Scale-Invariant Evolution
astro-ph.CO 2013-04 conditional novelty 5.0 of 10

Using the velocity-dependent one-scale model instead of assuming scale-invariant network evolution raises the predicted peak amplitude and broadness of the cosmic string gravitational wave background, which would tigh...
Study of gravitational radiation from cosmic domain walls
astro-ph.CO 2011-02 conditional novelty 5.0 of 10

Domain walls produce a nearly flat, slightly red-tilted gravitational wave spectrum between the Hubble scale at decay and the wall width, with the slope changing at both scales.
Bayesian Forecasts on Cosmic Superstring Searches with LISA
hep-ph 2026-08 conditional novelty 4.0 of 10

With simulated LISA data, cosmic superstring parameters Gµ and P remain strongly degenerate except in loud, small-P regions where a cusp-kink shape mixture can be distinguished.
Gravitational Waves from Multiple First-Order Phase Transitions in a Scenario with Early Matter Domination
hep-ph 2026-07 unverdicted novelty 4.0 of 10

Early matter domination with time-dependent decay rates produces multiple first-order phase transitions whose gravitational wave signatures encode the transition and reheating temperatures.
Upper Limits on the Isotropic Gravitational-Wave Background from the first part of LIGO, Virgo, and KAGRA's fourth Observing Run
gr-qc 2025-08 accept novelty 4.0 of 10

No gravitational-wave background is detected in O1-O4a data; the new CBC-spectrum limit Ω_GW(25 Hz) = 2.0×10^-9 (95%) is 1.7x tighter and remains roughly 2-3x above the GWTC-4-predicted astrophysical background of 0.9×10^-9.
All-sky search for short gravitational-wave bursts in the first part of the fourth LIGO-Virgo-KAGRA observing run
astro-ph.HE 2025-07 conditional novelty 4.0 of 10

An all-sky search of O4a LIGO data finds no new gravitational-wave bursts and improves burst sensitivity and rate limits by factors of 2 to 10 over the previous run.
Evolution of interior entropy of a loop quantum-corrected black hole pierced by a cosmic string
gr-qc 2024-12 conditional novelty 4.0 of 10

For a large-mass loop-quantum-corrected black hole pierced by a cosmic string, the paper derives the evolution relation between interior entropy and Bekenstein-Hawking entropy and shows the total satisfies the second law.
Implications for the Supermassive Black Hole Binaries from the NANOGrav 15-year Data Set
astro-ph.CO 2023-07 conditional novelty 4.0 of 10

Fitting an astro-informed SMBHB population model to NANOGrav 15-year data prefers large initial orbital eccentricity, and the same model extrapolated to millihertz frequencies predicts a detectable background for LISA...
Probing the Universe through the Stochastic Gravitational Wave Background
astro-ph.CO 2018-07 conditional novelty 4.0 of 10

For a stochastic gravitational wave background whose spectral slope changes inside the detector band, a broken power-law template fits far better than a single power law and lets aLIGO-aVirgo-KAGRA and DECIGO measure ...
New limits on cosmic strings from gravitational wave observation
astro-ph.CO 2017-09 conditional novelty 4.0 of 10

Pulsar timing array limits, combined with a new simulation-based cosmic string gravitational-wave spectrum, bound the string tension at Gμ < 1.5×10⁻¹¹ (95% CL).
Cosmological Backgrounds of Gravitational Waves and eLISA/NGO: Phase Transitions, Cosmic Strings and Other Sources
gr-qc 2012-01 conditional novelty 4.0 of 10

Refined gravitational-wave spectra from first-order phase transitions and cosmic string networks indicate that eLISA could detect phase transitions near 10 TeV and string tensions down to Gμ about 10^-13 for standard ...
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.
Waveform Modelling for the Laser Interferometer Space Antenna
gr-qc 2023-11 unverdicted novelty 2.0 of 10

A review of existing waveform models for LISA sources and the challenges that must still be overcome.
Stochastic Gravitational Wave Backgrounds
gr-qc 2018-11 accept novelty 2.0 of 10

A comprehensive review of stochastic gravitational wave backgrounds, covering cosmological and astrophysical sources, detection methods from LIGO-Virgo to pulsar timing and the CMB, and current upper limits.
Seeking String Theory in the Cosmos
hep-th 2011-05 accept novelty 2.0 of 10

Cosmic superstrings can form and survive in brane-inflation models, and existing CMB, pulsar-timing, lensing and cosmic-ray data already bound their tension at roughly G mu < 6e-7, with suppressed intercommutation as ...
Physics, Astrophysics and Cosmology with Gravitational Waves
gr-qc 2009-03 accept novelty 2.0 of 10

The paper reviews the physics, sources, detectors, data analysis and scientific payoff of gravitational wave astronomy, forecasting that upgraded ground-based interferometers should reach regular detections around 2014.

How the literature uses it

121 arXiv papers cite this in 187 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 · 97 sentences without a confident label

Builds on it 3 papers

In this section we consider the GW emission from a cosmic superstring loop, and generalize the results of Damour and Vilenkin [ref] on the emission of gravitational bursts from standard loops without junctions.

Gravitational Wave Bursts from Cosmic Superstrings with Y-junctions · GW emission from cosmic superstrings with junctions · 1.00
In particular, the mechanism for the emission of gravitational and particle radiation from cusps on loops of cosmic string [ref] also applies to cusps on strings between junctions.

Cusps on cosmic superstrings with junctions · Phenomenology · 0.86
In a follow up paper [ref] , they have considered GW bounds on networks of cosmic superstrings allowing for smaller reconnection probabilities, as well as allowing for the length of newly formed loops to be a free parameter.

Seeking String Theory in the Cosmos · Gravitational waves · 0.84

Uses its method or tool 5 papers

This was pointed out in Refs. [ref] and we follow the formalism of Ref. [ref] .

Cosmological effects of decaying cosmic string loops with TeV scale width · Gravitational waves · 0.90
We should calculate the stochastic GW background spectrum using the following formulae [ref]

Gravitational waves from kinks on infinite cosmic strings · THE STOCHASTIC BACKGROUND OF GRAVITATIONAL WAVES FROM KINKS · 0.98
In this section we calculate the GW burst signal following the methods of Refs. [ref] together with the refinements of Refs. [ref] .

Gravitational Wave Bursts as Harbingers of Cosmic Strings Diluted by Inflation · Gravitational Wave Signals from String Loops · 0.99

Uses its data or values 2 papers

Equation 4.8 in [ref] gives an analytic approximation to $h_c^cusp$ valid for small frequencies.

Gravitational wave signatures from kink proliferation on cosmic (super-) strings · Characteristic amplitude of stochastic background · 0.83
Pulsar timing, specifically, places a bound $Gμ<10^-7-10^-8$ on the cosmic string tension [ref] .

Edge Detection, Cosmic Strings and the South Pole Telescope · Introduction · 0.88

Compares with it 3 papers

The lines (solid or dotted/dashed) represent the graphs obtained using the DV interpolating functions, allowing for a direct comparison with [ref] .

The effect of extra dimensions on gravity wave bursts from cosmic string cusps · The gravitational waveform · 0.87
As expected, away from the junctions we recover the same GW signal as Damour and Vilenkin [ref] , both for a kink propagating on a string - for which $α=2/3$ and the emission occurs in a fan-like set of directions - as well as for a cusp, where $α=1/3$ and the emission occurs in a small cone around a particular direction.

Gravitational Wave Bursts from Cosmic Superstrings with Y-junctions · Conclusion · 0.89
This is in contrast with [ref] which focus on the burst of GW produced by the cusps and kinks.

Analytic Approaches to the Study of Small Scale Structure on Cosmic String Networks · Summary and discussion · 1.00

Cites it as support 1 paper

Furthermore, it has been shown that the background from cosmic strings could be dominated by a non-Gaussian contribution arising from the closest sources [ref] .

Detecting non-Gaussian gravitational wave backgrounds: a unified framework · Introduction · 0.97

Cites it as background 70 papers

Although the SGWB from SMBHBs is supposed to be the most promising source for the signal detected by the PTAs, the signal at nanoHertz can also originate from some cosmological processes [ref] , such as cosmological first-order phase transition [ref] , cosmic strings [ref] , domain walls [ref] , and scalar-induced GW [ref] accompanying the formation of primordial black holes [ref] .

Cosmological Interpretation for the Stochastic Signal in Pulsar Timing Arrays · Introduction · 0.95
The gravitational emission by cusps and kinks has been well-studied [ref] .

Periodic Fast Radio Bursts from Axion Emission by Cosmic Superstrings · Power of Axion Emission · 0.95
In addition to the SGWB, more recent bursts of GWs from cusps or kinks on string loops can potentially be resolved as individual events [ref] , but for standard scaling strings they are harder to find than the unresolved SGWB [ref] .

Gravitational Wave Bursts as Harbingers of Cosmic Strings Diluted by Inflation · Introduction · 0.84

Discussion

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