Binary inspiral, gravitational radiation, and cosmology

Lee Samuel Finn (Northwestern University)

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Binary inspiral, gravitational radiation, and cosmology

Lee Samuel Finn (Northwestern University)

General Relativity and Quantum Cosmology · Submitted 31 Jan 1996

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

The authors' main claim The distributions found here will play a pivotal role in testing cosmological models against our own universe and in constructing templates for the detection of cosmological inspiraling binary neutron stars and black holes.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.34 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.06 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Observations of binary inspiral in a single interferometric gravitational wave detector can be cataloged according to signal-to-noise ratio $\rho$ and chirp mass $\cal M$. The distribution of events in a catalog composed of observations with $\rho$ greater than a threshold $\rho_0$ depends on the Hubble expansion, deceleration parameter, and cosmological constant, as well as the distribution of component masses in binary systems and evolutionary effects. In this paper I find general expressions, valid in any homogeneous and isotropic cosmological model, for the distribution with $\rho$ and $\cal M$ of cataloged events; I also evaluate these distributions explicitly for relevant matter-dominated Friedmann-Robertson-Walker models and simple models of the neutron star mass distribution. In matter dominated Friedmann-Robertson-Walker cosmological models advanced LIGO detectors will observe binary neutron star inspiral events with $\rho>8$ from distances not exceeding approximately $2\,\text{Gpc}$, corresponding to redshifts of $0.48$ (0.26) for $h=0.8$ ($0.5$), at an estimated rate of 1 per week. As the binary system mass increases so does the distance it can be seen, up to a limit: in a matter dominated Einstein-deSitter cosmological model with $h=0.8$ ($0.5$) that limit is approximately $z=2.7$ (1.7) for binaries consisting of two $10\,\text{M}_\odot$ black holes. Cosmological tests based on catalogs of the kind discussed here depend on the distribution of cataloged events with $\rho$ and $\cal M$. The distributions found here will play a pivotal role in testing cosmological models against our own universe and in constructing templates for the detection of cosmological inspiraling binary neutron stars and black holes.

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	Observations of binary inspiral in a single interferometric gravitational wave detector can be cataloged according to signal-to-noise ratio $\rho$ and chirp mass $\cal M$.	background 0.92	0.12	0.03	asserted 0.99
s1	The distribution of events in a catalog composed of observations with $\rho$ greater than a threshold $\rho_0$ depends on the Hubble expansion, deceleration parameter, and cosmological constant, as well as the distribution of component masses in binary systems and evolutionary effects.	background 0.92	0.12	0.08	asserted 1.00
s2	In this paper I find general expressions, valid in any homogeneous and isotropic cosmological model, for the distribution with $\rho$ and $\cal M$ of cataloged events; I also evaluate these distributions explicitly for relevant matter-dominated Friedmann-Robertson-Walker models and simple models of the neutron star mass distribution.	contribution 0.99	0.97	0.29	asserted 1.00
s3	In matter dominated Friedmann-Robertson-Walker cosmological models advanced LIGO detectors will observe binary neutron star inspiral events with $\rho>8$ from distances not exceeding approximately $2\,\text{Gpc}$, corresponding to redshifts of $0.48$ (0.26) for $h=0.8$ ($0.5$), at an estimated rate of 1 per week.	result 1.00	0.81	0.21	asserted 0.88
s4	As the binary system mass increases so does the distance it can be seen, up to a limit: in a matter dominated Einstein-deSitter cosmological model with $h=0.8$ ($0.5$) that limit is approximately $z=2.7$ (1.7) for binaries consisting of two $10\,\text{M}_\odot$ black holes.	result 1.00	0.80	0.09	asserted 0.99
s5	Cosmological tests based on catalogs of the kind discussed here depend on the distribution of cataloged events with $\rho$ and $\cal M$.	interpretation 0.66	0.15	0.10	asserted 1.00
s6	The distributions found here will play a pivotal role in testing cosmological models against our own universe and in constructing templates for the detection of cosmological inspiraling binary neutron stars and black holes.	interpretation 0.90	0.53	0.42	asserted 0.95

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

Observations of binary inspiral in a single interferometric gravitational wave detector can be cataloged according to signal-to-noise ratio $\rho$ and chirp mass $\cal M$. The distribution of events in a catalog composed of observations with $\rho$ greater than a threshold $\rho_0$ depends on the Hubble expansion, deceleration parameter, and cosmological constant, as well as the distribution of component masses in binary systems and evolutionary effects. In this paper I find general expressions, valid in any homogeneous and isotropic cosmological model, for the distribution with $\rho$ and $\cal M$ of cataloged events; I also evaluate these distributions explicitly for relevant matter-dominated Friedmann-Robertson-Walker models and simple models of the neutron star mass distribution. In matter dominated Friedmann-Robertson-Walker cosmological models advanced LIGO detectors will observe binary neutron star inspiral events with $\rho>8$ from distances not exceeding approximately $2\,\text{Gpc}$, corresponding to redshifts of $0.48$ (0.26) for $h=0.8$ ($0.5$), at an estimated rate of 1 per week. As the binary system mass increases so does the distance it can be seen, up to a limit: in a matter dominated Einstein-deSitter cosmological model with $h=0.8$ ($0.5$) that limit is approximately $z=2.7$ (1.7) for binaries consisting of two $10\,\text{M}_\odot$ black holes. Cosmological tests based on catalogs of the kind discussed here depend on the distribution of cataloged events with $\rho$ and $\cal M$. The distributions found here will play a pivotal role in testing cosmological models against our own universe and in constructing templates for the detection of cosmological inspiraling binary neutron stars and black holes.

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References

Forward citations

Cited by 10 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 151 citations worldwide. Full citation record

Distinguishing Neutron Star vs. Low-Mass Black Hole Binaries with Late Inspiral & Postmerger Gravitational Waves $-$ Sensitivity to Transmuted Black Holes and Non-Annihilating Dark Matter
hep-ph 2025-07 unverdicted novelty 6.0 of 10

Future high-frequency-sensitive GW detectors can distinguish binary neutron star from low-mass black hole mergers in late phases, enabling separation of merger rates and constraints on heavy non-annihilating dark matt...
Bayesian Evidence for Both Astrophysical and Primordial Black Holes: Mapping the GWTC-2 Catalog to Third-Generation Detectors
astro-ph.CO 2021-02 conditional novelty 6.0 of 10

A mixed astrophysical plus primordial black hole population fits the GWTC-2 catalog better than the LIGO/Virgo truncated astrophysical model alone, with about one in five mergers ascribed to primordial binaries.
Spin orientations of merging black holes formed from the evolution of stellar binaries
astro-ph.HE 2018-08 conditional novelty 6.0 of 10

Black-hole binary spin misalignments split into three precession morphologies whose relative fractions track whether stellar tides realigned a spin before the second core collapse, giving a measurable handle on massiv...
Reinterpreting Low Frequency LIGO/Virgo Events as Magnified Stellar-Mass Black Holes at Cosmological Distances
astro-ph.CO 2018-02 conditional novelty 6.0 of 10

The four highest-mass LIGO binary black hole events are reinterpreted as gravitationally lensed stellar-mass binaries at redshift 1 to 3, with magnifications of order 100.
Formation and Detectability of PSR J0653+0443-like Extremely Eccentric Binary Neutron Stars in the Milky Way
astro-ph.HE 2026-10 conditional novelty 5.0 of 10

Only about 0.6% of Milky Way binary neutron stars detectable by FAST should have orbital eccentricity above 0.99, so PSR J0653+0443 is rare but consistent with standard binary evolution.

Show 5 more citing papers

Prospect for Detection of Strongly Lensed Multi-messenger Signals of Binary Neutron Star Mergers
astro-ph.HE 2026-07 conditional novelty 5.0 of 10

Future CE+ET detectors may detect lensed BNS kilonovae at ~0.5/yr via pointed follow-up of known galaxy lenses, while lensed sGRBs and afterglows remain rare or undetectable with current-generation facilities.
Constraining the primordial black hole scenario with Bayesian inference and machine learning: the GWTC-2 gravitational wave catalog
gr-qc 2020-11 conditional novelty 5.0 of 10

Assuming every GWTC-2 black hole merger is primordial, the authors infer that primordial black holes make up about 0.3 percent of dark matter and that accretion, not formation, supplies the observed spins.
Multiband gravitational-wave event rates and stellar physics
astro-ph.HE 2019-01 conditional novelty 5.0 of 10

Combining LISA and ground-detector selection effects, the authors forecast a few to tens of joint black-hole merger detections, limited by LISA's horizon rather than by ground sensitivity.
Precise LIGO Lensing Rate Predictions for Binary Black Holes
astro-ph.CO 2017-03 conditional novelty 5.0 of 10

LIGO should detect roughly 0.2 lensed binary black hole mergers per year at O1 sensitivity and about 14 per year at design sensitivity, with the quoted uncertainty dominated by the assumed local merger rate rather tha...
Inferring the properties of a population of compact binaries in presence of selection effects
astro-ph.IM 2020-07 unverdicted novelty 2.0 of 10

Pedagogical derivation from first principles of hierarchical Bayesian inference for population properties of compact binaries in the presence of selection effects, with two worked examples.

How later papers used it

60 later papers cite it

Evidence: substantial. 60 of the citing papers share no author with it, and 26 of those carry a confident label from Pith's citation classifier.

Pith read 18 of the 100 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

5 later papers by other authors are listed below: 5 used its method or tool.

Uses its method or tool 5 of 26 papers with this label

Used the gravitational wave detection theory developed by this paper to translate the intrinsic merger rate into the detectable source rate.

Gravitational lensing of gravitational waves: A statistical perspective (2018) · 1.00 · paraphrased: the licence does not allow quoting
Used this paper's conditional probability distribution of signal-to-noise ratio at redshift and chirp mass in its merger rate density expression.

Probing the nature of dark matter via gravitational waves lensed by small dark matter halos (2022) · 0.81 · paraphrased: the licence does not allow quoting
Used this paper's formalism to describe the response of an interferometric detector to gravitational radiation from an inspiraling binary.

Hubble without the Hubble: cosmology using advanced gravitational-wave detectors alone (2011) · 1.00 · paraphrased: the licence does not allow quoting
Followed this paper to write the matched filtering signal-to-noise ratio in a single detector.

Cosmology with the lights off: Standard sirens in the Einstein Telescope era (2012) · 0.95 · paraphrased: the licence does not allow quoting
Estimated each recorded gravitational wave event's detection probability using the semi-analytic approach by another work and this paper.

High mass but low spin: an exclusion region to rule out hierarchical black-hole mergers as a mechanism to populate the pair-instability mass gap (2021) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

34 arXiv papers cite this in 58 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 · 34 sentences without a confident label

Uses its method or tool 13 papers

Here we follow a common approach and approximate $p_det(θ)$ using the single-detector semi-analytic approximation of Refs. [ref] ) as implemented in Ref. [ref] with a signal-to-noise ratio threshold equal to 8 and the waveform model of Ref. [ref] .

Machine-learning interpolation of population-synthesis simulations to interpret gravitational-wave observations: a case study · Hierarchical Bayesian inference · 1.00
where $R_mrg(ℳ_0;z)=p(ℳ_0|z)R_mrg(z)$ is the merger rate density (MRD) for events with chirp mass $ℳ_0$ at $z$ [ref] , and $P_ϱ(ϱ|z,ℳ_0)$ is the conditional probability distribution of SNR at $z$ and $ℳ_0$ [ref] .

Probing the nature of dark matter via gravitational waves lensed by small dark matter halos · High frequency band · 0.81
We estimate $ $ with the widely used single-detector semianalytic approximation of Refs.~ [ref] , as implemented in the Python package gwdet~ [ref] , which relies on computing the SNR of optimally oriented sources with the same intrinsic parameters.

Deep learning and Bayesian inference of gravitational-wave populations: Hierarchical black-hole mergers · Detection probability · 1.00

Cites it as background 5 papers

Population inference also enables the measurement of cosmological parameters under the assumption that the intrinsic distribution exhibits negligible redshift evolution [ref] .

Emergent structure in the binary black hole mass distribution and implications for population-based cosmology · Cosmological inference · 0.84
Other methods for cosmological inference (see [ref] ) have been proposed for BNS systems that do not rely on any redshift measurements.

Astrophysical calibration of gravitational-wave detectors · Binary neutron star standard sirens · 0.97
The sky sensitivity of the detector (as encoded in $w_ℓm$) can affect the detectability of individual modes (see [ref] for a discussion of this issue in the context of inspiral, and [ref] for a nice overview of the nomenclature and conventions used in the gravitational-wave literature).

Multi-mode black hole spectroscopy · Response redshift and detectability fraction · 0.99

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