Integrated cosmological memory: A dark-siren method to probe dark energy

Archana Pai; Indranil Chakraborty; Sayantan Ghosh; S. Shankaranarayanan; Susmita Jana

REVIEW 4 major objections 5 minor 58 references

Integrated cosmological memory: A dark-siren method to probe dark energy

T0 review · 4 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper proposes that the integrated cosmological memory offset imprinted on a single gravitational-wave signal, combined with the standard luminosity-distance measurement, breaks the distance–redshift degeneracy entirely within the grav

desk verdict The dual-observable idea is genuinely worth pursuing, but this manuscript leans on self-cited formulas, missing supplementary material, and an unpublished reference; send it to review but expect major revision. read the letter →

arxiv 2608.03739 v1 pith:KXS3Z46D submitted 2026-08-04 astro-ph.CO gr-qchep-th

Indranil Chakraborty , Sayantan Ghosh , Susmita Jana , Archana Pai , S. Shankaranarayanan This is my paper · ORCID

classification astro-ph.COgr-qchep-th

keywords gravitational-wavecosmologydarksirensgravitationalwavememoryenergyequationofstateHubbletensionluminositydistancenext-generationdetectorsintegratedcosmological

topics Dark Energy The Hubble Tension

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Standard gravitational-wave cosmology is stuck between bright sirens that need a rare electromagnetic counterpart and dark sirens that depend on host-galaxy catalogs which are incomplete at high redshift. This paper proposes a third route: expanding spacetime imprints a cumulative 'integrated cosmological memory' on the wave, a step-like offset that depends on a different integral of cosmic history than the luminosity distance. By measuring both the chirp's distance and the memory offset from a single merger, the authors argue the distance–redshift degeneracy is broken using gravitational data alone. Injections into simulated next-generation detector noise show that one loud event can constrain the expansion parameter B to about 12–16%, and the result shifts by only ~4% when H0 is varied between 67 and 73 km/s/Mpc. The payoff is a catalog-free, purely gravitational probe of late-time dark energy that is nearly immune to the Hubble tension.

What carries the argument

The central object is the integrated cosmological memory (ICM), Eq. (1), together with the memory ratio R = A/h⊕ obtained by matched filtering the high-passed post-merger step against the peak CBC amplitude. The scheme uses the B-parametrization E^2(z)=Ωm0(1+z)^{2/B}+(1−Ωm0) to map expansion histories onto a single parameter, then reads B off a precomputed R–dL surface, exploiting the fact that the memory has a high-passed step morphology, distinct from the chirping signal, so a dedicated transient search can isolate it after subtracting the CBC waveform.

What would settle it

Compute the memory waveform for a compact binary coalescence in an expanding FLRW background using full numerical relativity or a higher-order post-Newtonian model, and check whether the late-time offset follows Eq. (1) and rises on a timescale of about 0.01 s; if the offset is absent or the rise time is much longer, the injected template does not match reality and the claimed 12–16% B constraints are not measurable.

Watch

Extended reading notes

Core claim

The central claim is that the observed gravitational-wave strain from a compact binary merger contains two separable cosmological observables: the luminosity distance dL from the oscillatory part of the signal, and the integrated cosmological memory (ICM) offset from the post-merger step. The ICM amplitude follows N+ = h⊕/(3 E^{2/3}(z0)) ∫0^{z0} (1+z)/E^{4/3}(z) dz, where E(z)=H(z)/H0; because this integral weights the expansion history differently than dL does, the pair (dL, R=N+/h⊕) lands on a unique point in the R–dL plane for each expansion history, fixing both distance and redshift for a single event. The authors demonstrate the extraction in simulation: standard Bayesian parameter esti

Load-bearing premise

The argument rests on the assumption that the integrated cosmological memory is exactly the high-passed sigmoid of Eq. (2) with amplitude given by Eq. (1) and a 0.01 s rise time, taken from the authors' prior work; if the true cosmological memory is smaller, differently shaped, or absent, the dual-observable extraction and the claimed constraints do not hold.

Editorial extensions

If this is right

A single loud high-redshift merger observed by a next-generation ground-based network can simultaneously yield luminosity distance and integrated memory, breaking the distance–redshift degeneracy without any electromagnetic counterpart or galaxy catalog.
The expansion parameter B is recovered to 12–16% per event, with at most ~4% variation when H0 is changed between 67 and 73 km/s/Mpc, making the probe largely insensitive to Hubble-tension systematics.
The method distinguishes a quintessence-like expansion history (B=1/2) from ΛCDM (B=2/3) even with a single event; distinguishing B=3/4 is harder, especially at smaller distances where the memory ratios converge.
Stacking many events from a next-generation network is expected to tighten the constraints well below single-event precision, since the approach is catalog-free and applies to every high-redshift merger.
Mapping the recovered B to the CPL equation-of-state parameters yields medians consistent with (−1,0) for ΛCDM injections, with a known projection offset at z≈1.4 that reflects the non-linearity of the transformation rather than a bias in the gravitational-wave measurement.

Reading between the lines

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

If Eq. (1) holds, the same integrated-memory observable could also accumulate deviations from general relativity, so the technique might be adapted to constrain modified gravity or gravitational-wave propagation effects; the paper hints at this but does not test it.
The assumed 0.01 s memory rise time is a free input; if the true memory rises over a longer timescale or overlaps with the ringdown, the matched-filter template would need to include ringdown rejection, and the claimed 12–16% per-event precision could be optimistic.
Because the memory signal becomes large and cosmologically distinct only at dL≳10 Gpc, the method's practical reach is at z≳1, exactly where supernova-based dark-energy probes are weakest, making ICM complementary to the standard distance-ladder approach.
The near-H0-independence of the B constraint suggests a possible independent route to the Hubble tension: measuring B from integrated memory and separately measuring dL at low redshift could calibrate H0 without the cosmic distance ladder.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's my read. The genuinely new thing is the proposal to use the integrated cosmological memory (ICM) as a second, catalog-free observable in GW cosmology, so that a single event gives both dL and a memory offset that depends on the expansion history in a distinct way. That's a real idea, and the paper works through the pipeline carefully: injections with two third-generation networks, posteriors recover the injected CBC parameters within 90% credible intervals, and the check that the recovered B varies by only a few percent with H0 between 67 and 73 is a nice touch. The treatment of sky location, the mask to avoid a singular antenna matrix, and the book-keeping from SNR to offset are sensible.

The central physics, though, is not in this paper. Eq. (1), the ICM amplitude law, is taken from the authors' previous papers (Chakraborty et al. 2025a,b), and those papers are not re-derived or even summarized here. The time-domain model, a high-passed sigmoid with tau = 0.01 s, is also assumed. The injection-recovery tests re-inject exactly that model, so they demonstrate internal consistency, not agreement with nature. If the true memory amplitude or morphology differs, everything downstream is biased. That is a load-bearing caveat, and the paper does not engage with it beyond a footnote. The mapping from B to w(z) relies on Eq. (7) tied to an unpublished reference (Sharma et al., with a blank arXiv number), and there is a missing equation number in the text. The supplementary information is promised but not included. And 'completely breaks' in the abstract oversells what is a proof-of-principle with 12-16% per-event constraints and a fair amount of B=2/3 vs B=3/4 degeneracy.

None of these are fatal in principle — they are fixable, and if the previous ICM papers are right, this is a meaningful step toward a dark-siren probe. But the current manuscript is not self-contained enough for publication as written. It deserves a serious referee, but the referee should be sent to the earlier papers too, and the revision should either derive or carefully summarize the ICM formalism, include the SI, replace the unpublished citation, and soften the claim of complete degeneracy breaking.

Referee Report

4 major / 5 minor

Summary. The paper proposes a dark-siren cosmological method based on the 'Integrated Cosmological Memory' (ICM): the cumulative memory strain accumulated by a gravitational wave propagating through the expanding universe. The authors claim that measuring both the standard luminosity distance from the CBC transient and the ICM offset from the same event breaks the distance–redshift degeneracy without electromagnetic counterparts or galaxy catalogs. They inject a BBH signal plus a high-passed sigmoid memory transient into simulated CE–CE–ET and CE–CE–LI networks, recover CBC parameters with Bayesian PE, estimate the memory offset by matched filtering the residual, form a memory ratio R, and map R–dL to a phenomenological expansion parameter B. They report 12–16% per-event constraints on B, weak dependence on H0 (≤4% variation), and unbiased recovery of injected CBC parameters at 90% credible intervals.

Significance. If Eq. (1) is correct, the idea is novel and potentially important: it offers a purely gravitational, catalog-free route to high-redshift cosmology and dark energy. The paper's injection campaign is self-consistent and carefully executed: recovered CBC parameters fall inside 90% credible intervals, the H0 sensitivity check is a useful and well-posed test, and the two-detector polarization inversion for the memory offset is clearly formulated. The strength is in the proof-of-principle pipeline, not in the physics of the memory law itself. However, the scientific payoff is entirely conditional on an imported, unvalidated amplitude law and an assumed signal morphology. Because the injection-recovery tests re-inject the same model, they cannot validate the physical input. The significance is therefore real but conditional; the manuscript needs to make the central law accessible and testable before the claims can be fully assessed.

major comments (4)

[Section 1, Eq. (1)] The central amplitude law N+ = h⊕/(3E^{2/3}(z0)) ∫0^{z0} (1+z)/E^{4/3}(z) dz is imported from Chakraborty et al. 2025a,b, but is not derived in this manuscript. The entire dual-observable scheme, the R–dL mapping, and the B constraints rest on this equation. The injection campaign uses the same relation to generate and analyze the data, so it cannot provide independent support. This is a load-bearing correctness-risk concern. Please either derive Eq. (1) in the paper, or give a self-contained summary of the derivation and a check against known limits (e.g., the asymptotically flat memory limit and any available FLRW numerical results). Without this, a reader cannot judge whether the claimed 'completely breaks the degeneracy' statement applies to the physical universe or only to the assumed model.
[Section 2, 'Parameter recovery for CBC source' and Fig. 4] The inference of B is not a full joint Bayesian estimate. The paper itself notes that the R distribution is a 'loose posterior' obtained by combining Bayesian and frequentist point estimates, and that the B values are read off a theoretical grid. This is a legitimate proof-of-principle, but it does not substantiate the abstract's claim that 'extracting both observables from a single binary merger completely breaks the distance-redshift degeneracy.' In particular, the analysis fixes H0, uses a known sky location, assumes the waveform model, and assumes the memory morphology. A joint posterior on (dL, B) — or at least an explicit propagation of the dL uncertainties and their covariance with R into B — is needed to support the 'completely breaks' language. As it stands, the claim is conditional on the assumed model and on the chosen analysis configuration.
[Section 3, Eq. (7)] The mapping from the phenomenological parameter B to the dark-energy equation of state w(z;B) is a central part of the dark-energy claim, but the derivation is not shown: the manuscript refers to 'matching our parameterization (??)' and to an unpublished reference (Sharma et al. ????). The low-redshift Taylor expansion to (w0, wa) then produces numerical values that the authors concede are biased by nonlinear projection. This part of the paper is not load-bearing for the injection-recovery results, but it is a central scientific payoff. Please provide the derivation of Eq. (7) and a proper reference, or state clearly that the EoS mapping is a heuristic interpretation that is not the main result.
[Appendix A and Section 2, Eq. (2)] Two physical assumptions are made without adequate support. First, the memory template is assumed to be a high-passed sigmoid with rise time τ=0.01 s; the sensitivity of the recovered B constraints to τ and to the chosen filter cutoff is not explored. Second, the paper states that for the face-on configuration 'the intrinsic (Christodoulou) nonlinear memory identically vanishes,' so that the injected memory is 'pure ICM.' This statement needs a derivation or a reference; if the vanishing is not exact, the injected signal is contaminated by source memory and the 'pure ICM' interpretation fails. Even if the step is a reasonable approximation, the paper should quantify how morphology mismodeling affects the matched-filter estimate of A and the resulting B constraints.

minor comments (5)

[References] The supplementary information is cited as (I. Chakraborty et al. ????) with no year or preprint number, and Sharma et al. is cited as 'arXiv:' with no identifier. The paper cannot be fully evaluated without these references; please complete them.
[Section 3, text after Eq. (7)] The phrase 'matching our parameterization (??)' contains an unresolved equation number; it should refer to Eq. (A1) or a numbered equation in the main text.
[Appendix, Table 1] There is a typo 'T able 1' in the caption. Also, 'Bestimates' in the text above Table 2 should be 'B estimates'.
[Throughout] The Hubble constant appears inconsistently as 'H0', 'H 0', and 'H_0'. Please use a single notation consistently.
[Figure 4 caption] The caption states that the x-axis shows 'the recovered network SNR ... of the memory signal' and the y-axis shows 'the recovered B constraints.' Please clarify whether the plot shows multiple subpanels or a scatter plot, and define the uncertainty bars in the x direction.

Circularity Check

2 steps flagged · score 4.0 of 10

ICM amplitude law (Eq. 1) is imported from the authors' own prior work and the injection campaign re-injects the same relation used for the R–dL → B mapping, so the quantitative demonstration is self-consistency rather than an independent test; the central 'degeneracy breaking' claim remains conditional on that self-cited law.

self citation load bearing [Section 1, Eq. (1) and surrounding text (page 2)]
"In this article, we propose that the Integrated Cosmological Memory (ICM) (I. Chakraborty et al. 2025a,b) — embedded in the post-merger phase of the GW transient signal — is the key to unlocking this probe... recent theoretical advancements have established a rigorous framework for GW memory in FLRW geometries (I. Chakraborty et al. 2025a,b). This formalism reveals that the memory strain contains a unique, cumulative contribution of the cosmological background."

The load-bearing ICM amplitude law, Eq. (1): N+ = h⊕/(3E^{2/3}(z0)) ∫ (1+z)/E^{4/3}(z) dz, is taken directly from the authors' previous papers via self-citation and is not re-derived or independently validated in this manuscript. Every later conclusion—the claimed dL–z degeneracy breaking, the R–dL relation in Fig. 2, the recovered B constraints, and the H0-insensitivity statement—is computed from this same self-cited formula. The central premise of the paper therefore rests on a self-citation chain rather than on an independent derivation presented here.
other [Section 2 (Methods), Eq. (2) and Fig. 2 mapping]
"Using an injection campaign containing full astrophysical GW waveforms (compact binary transients plus the ICM) into simulated nG detector noise, we isolate the cosmological contribution to the memory strain: h_mem(t,z0)=N(z0)σ(t); σ(t)=[1+e^{−(t−t0)/τ}]^{−1}... Finally, to map the recovered 90% credible intervals of R and dL onto the B-parameterized theoretical surface as illustrated in the R−dL plane in Fig. (2)..."

The injected memory signals are generated from the same Eq. (1) with an assumed B, and then the recovered R–dL intervals are interpreted using the B-parameterized theoretical surface also derived from Eq. (1). Thus the recovered B approximately equaling the injected B—and the quoted 12–16% per-event constraints—demonstrate that the pipeline can recover what was put in, not that the physical ICM law is correct. This is a circular validation of the method, standard for injection studies, but it does not independently validate the assumed ICM relation; the numerical forecast is built from the same equation that defines the observable–cosmology mapping.

full rationale

The paper's central theoretical claim—that one can extract both dL and the integrated cosmological memory from a single merger and thereby break the distance–redshift degeneracy—is a genuine consequence of Eq. (1), provided that equation is correct. However, Eq. (1) is imported, not re-derived, from the authors' own prior works (Chakraborty et al. 2025a,b), making that self-citation load-bearing. Moreover, the simulation/injection campaign is a self-consistency loop: the injected memory uses the same N(z0) formula that is later used to map the recovered R onto B. This is not a damning circularity in the sense of a fitted parameter being renamed a prediction; it is normal injection-test practice and the paper does present the work as a proof-of-principle. Still, the reader should recognize that the 12–16% per-event B constraints and the 'completely breaks the degeneracy' language are conditional on the assumed, self-cited ICM law and on the high-passed sigmoid morphology of Eq. (2); if the true cosmological memory is smaller, morphologically different, or contaminated by other memory contributions, those conclusions would not follow. The paper also acknowledges that no waveform models currently include both the CBC and the ICM signal, and that the 'actual memory signal, as predicted by GR is a step-like function' is an assumption. Considering these issues, a moderate score of 4 reflects that the central claim has independent mathematical content conditional on the imported equation, but the supporting demonstration is partially circular and relies heavily on self-citation.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

The analysis carries three assumed inputs: the self-cited ICM amplitude law, the step-like waveform model with an assumed rise time, and the Sen-Sethi parametrization with an unstated Omega_m0. The central claim would collapse if any of these differ from nature.

free parameters (3)

Memory rise time tau = 0.01 s
Set from the dynamical time of the ~300 solar mass source and used to build the normalized matched-filter memory template; recovered amplitude and SNR depend on this assumed value.
Omega_m0 = not stated
The Sen-Sethi E(z) parameterization in Appendix A contains Omega_m0, which is never given a value in the text; the injections and the dL-to-z mapping must assume some fiducial matter density, likely 0.3.
High-pass filter cutoff = 5 Hz (CE/ET), 10 Hz (LI)
Fixed filter choices that shape the memory transient template; different cutoffs would change the matched-filter SNR and the recovered offset.

assumptions (5)

ad hoc to paper Integrated cosmological memory formula Eq (1)
The central amplitude law N+ = h⊕/(3E^{2/3}) ∫ (1+z)/E^{4/3} dz is lifted from the authors' own PRD papers (Chakraborty et al. 2025a,b) and is not re-derived or externally validated here.
domain assumption Memory waveform is a step with known rise time
Eq (2) models h_mem(t) = N(z0) [1+exp(-(t-t0)/tau)]^{-1} and assumes tau is known; the matched-filter template is built from this model.
domain assumption Face-on non-spinning BBH has zero Christodoulou memory
Stated in the Methods/Results section as the reason the injected memory is 'entirely zero at the source'; the extraction pipeline relies on this to isolate ICM.
domain assumption Stationary Gaussian detector noise, negligible waveform subtraction residual
The likelihood and matched-filter noise model assume Gaussian stationary noise, and the residual after subtracting the best-fit CBC waveform is treated as sub-dominant leakage; real noise, glitches, and waveform systematics are not modeled.
domain assumption Flat FLRW + Sen-Sethi phenomenological E(z)
The B-dependent expansion history E^2(z) = Omega_m0(1+z)^{2/B} + (1-Omega_m0) is assumed to capture dark energy; it is a phenomenological fitting form, not derived from an action.

invented entities (1)

Integrated Cosmological Memory (ICM)
purpose: Provides a second gravitational observable, the cumulative strain offset, that depends on the integrated expansion history and breaks the dL-z degeneracy.
The ICM is a theoretically predicted effect from the authors' prior work; it has not been detected independently, and this paper's injections generate the signal from the same model used for inference.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Integrated cosmological memory: A dark-siren method to probe dark energy." pith.science (2026). https://pith.science/paper/KXS3Z46D

@misc{pith2026260803739,
  author       = {Pith},
  title        = {Pith review of: Integrated cosmological memory: A dark-siren method to probe dark energy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KXS3Z46D}},
  note         = {Machine review of arXiv:2608.03739}
}

read the original abstract

Gravitational-wave (GW) cosmology is currently bottlenecked by the scarcity of electromagnetic counterparts for bright sirens and the systematic uncertainties of galaxy catalogs for dark sirens. We propose a purely gravitational resolution using the Integrated Cosmological Memory (ICM)-the cumulative GW strain encoded in the spacetime geometry of an expanding Universe. While the GW transient emitted by the source provides the luminosity distance, the ICM accumulates a mathematically distinct integral of the cosmic expansion history. We demonstrate that extracting both observables from a single binary merger completely breaks the distance-redshift degeneracy within the gravitational sector. This establishes a novel, catalog-free dark siren framework for third-generation GW detector networks. Crucially, the resulting constraints on late-time dark energy are only weakly sensitive to the local expansion rate, providing a robust cosmological probe that can potentially mitigate the impact of the H0 tension.

Figures

Figures reproduced from arXiv: 2608.03739 by the authors.

**Figure 2.** The ICM memory ratio R as a function of dL (for H0 = 70 km s−1Mpc −1 ) and the expansion parameter B (color scale). Inset: The 90% credible intervals of dL and R are denoted by the solid green lines. The simulated injection at dL = 10 Gpc assuming ΛCDM (B = 2/3) is shown by the red dot. 2. METHODS In the detector bandwidth, the GW strain is the sum of the CBC signal hcbc(t), the detector noise n(t) and the high-pass… view at source ↗

**Figure 3.** Parameter recovery for the CE-CE-ET network at [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: The x-axis shows the recovered network SNR (with uncertainties arising because of the stochastic [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: CE-CE-ET network: Posterior distributions of luminosity distance dL (top row), mass ratio q (middle row), and chirp mass Mc (bottom row) for signals injected at different distances [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: CE-CE-LI network: Posterior distributions of luminosity distance dL (top row), mass ratio q(middle row) and chirp mass Mc (bottom row). The posteriors shown in the left, middle and right columns are for the signals injected at dL = 5 Gpc, 8 Gpc, 10 Gpc respectively. Ea…

**Figure 7.** Figure 7: Plots of the sky location posteriors. The top panel shows the sky location posteriors for the CE-CE-ET network, and the bottom panel shows the sky location posteriors for the CE-CE-LI network, for B = 1 2 at dL = 5GPc. The blue cross shows the injected right ascension …

**Figure 8.** Figure 8: The CBC signal at distance = 5 Gpc in the time domain overlaid on the ICM signal corresponding to B = 1 2 . The actual memory signal, as predicted by the GR is a step-like function (cyan dashed). The signal observed in the detector noise will be high-passed version (sh…

**Figure 9.** Figure 9: The left column shows the variations of the determinant of the F-matrix for H1 and L1 detectors (upper panel) and H1 and V1 detectors (lower panel) across the entire sky. The right panel shows the variations of the antenna response ( p f 2 p + f 2 c ) across the entire…

**Figure 10.** Figure 10: Plots used to read off memory offset from the estimated matched-filter SNR with the memory template. The black solid curve shows the variation of the optimal SNR with the memory offset. The shaded green region shows the 90% confidence region around the optimal SNR. Fo…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

58 extracted references · 19 canonical work pages

[1]

2016, Phys

Abbott, B., et al. 2016, Phys. Rev. Lett., 116, 061102, doi: 10.1103/PhysRevLett.116.061102

doi:10.1103/physrevlett.116.061102 2016
[2]

P., et al

Abbott, B. P., et al. 2016, Phys. Rev. Lett., 116, 221101, doi: 10.1103/PhysRevLett.116.221101

doi:10.1103/physrevlett.116.221101 2016
[3]

P., et al

Abbott, B. P., et al. 2017a, Phys. Rev. Lett., 119, 161101, doi: 10.1103/PhysRevLett.119.161101

doi:10.1103/physrevlett.119.161101
[4]

P., et al

Abbott, B. P., et al. 2017b, Nature, 551, 85, doi: 10.1038/nature24471

doi:10.1038/nature24471
[5]

P., et al

Abbott, B. P., et al. 2017c, Astrophys. J. Lett., 848, L12, doi: 10.3847/2041-8213/aa91c9

doi:10.3847/2041-8213/aa91c9
[6]

2023, Phys

Abbott, R., et al. 2023, Phys. Rev. X, 13, 011048, doi: 10.1103/PhysRevX.13.011048

doi:10.1103/physrevx.13.011048 2023
[7]

2022, JHEAp, 34, 49, doi: 10.1016/j.jheap.2022.04.002

Abdalla, E., et al. 2022, JHEAp, 34, 49, doi: 10.1016/j.jheap.2022.04.002

doi:10.1016/j.jheap.2022.04.002 2022
[8]

2020, Astron

Aghanim, N., et al. 2020, Astron. Astrophys., 641, A6, doi: 10.1051/0004-6361/201833910

doi:10.1051/0004-6361/201833910 2020

Show all 58 references

[9]

2019, Astrophys

Ashton, G., et al. 2019, Astrophys. J. Suppl., 241, 27, doi: 10.3847/1538-4365/ab06fc

2019 doi
[10]

P., & Shankaranarayanan, S

Bansal, P., Johnson, J. P., & Shankaranarayanan, S. 2025, Phys. Rev. D, 112, 124078, doi: 10.1103/5qnb-ldfl

2025 doi
[11]

Berti, E., Cardoso, V., & Will, C. M. 2006, Phys. Rev. D, 73, 064030, doi: 10.1103/PhysRevD.73.064030

2006 doi
[12]

2016, Phys

Belczynski, K. 2016, Phys. Rev. Lett., 117, 101102, doi: 10.1103/PhysRevLett.117.101102

2016 doi
[13]

2017, Class

Bieri, L., Garfinkle, D., & Yunes, N. 2017, Class. Quant. Grav., 34, 215002, doi: 10.1088/1361-6382/aa8b52

2017 doi
[14]

M., Nichols, D

Boersma, O. M., Nichols, D. A., & Schmidt, P. 2020, Phys. Rev. D, 101, 083026, doi: 10.1103/PhysRevD.101.083026

2020 doi
[15]

B., & Thorne, K

Braginskii, V. B., & Thorne, K. S. 1987, Nature (London), 327, 123, doi: 10.1038/327123a0

1987 doi
[16]

2025a, Phys

Chakraborty, I., Jana, S., & Shankaranarayanan, S. 2025a, Phys. Rev. D, 111, 083548, doi: 10.1103/PhysRevD.111.083548

doi
[17]

2025b, Phys

Chakraborty, I., Jana, S., & Shankaranarayanan, S. 2025b, Phys. Rev. D, 112, L021503, doi: 10.1103/fb3l-16w6

doi
[18]

2001, Int

Chevallier, M., & Polarski, D. 2001, Int. J. Mod. Phys. D, 10, 213, doi: 10.1142/S0218271801000822

2001 doi
[19]

2017a, Class

Chu, Y.-Z. 2017a, Class. Quant. Grav., 34, 035009, doi: 10.1088/1361-6382/34/3/035009

doi
[20]

J., Lundgren, A

Davis, D., Massinger, T. J., Lundgren, A. P., et al. 2019, Class. Quant. Grav., 36, 055011, doi: 10.1088/1361-6382/ab01c5 Di Valentino, E., Mena, O., Pan, S., et al. 2021, Class. Quant. Grav., 38, 153001, doi: 10.1088/1361-6382/ac086d Di Valentino, E., et al. 2025, Phys. Dark ...

2019
[21]

2010, Class

Favata, M. 2010, Class. Quant. Grav., 27, 084036, doi: 10.1088/0264-9381/27/8/084036

2010 doi
[22]

Ferraro, S., & Wilson, M. J. 2019, Bulletin of the AAS, 51

2019
[23]

L., & CEERS Collaboration

Finkelstein, S. L., & CEERS Collaboration. 2025, Astrophy. J. Letts., 983, L4, doi: 10.3847/2041-8213/adbbd3

2025 doi
[24]

E., & Farr, W

Fishbach, M., Holz, D. E., & Farr, W. M. 2018, Astrophys. J. Lett., 863, L41, doi: 10.3847/2041-8213/aad800

2018 doi
[25]

2019, Astrophys

Fishbach, M., et al. 2019, Astrophys. J. Lett., 871, L13, doi: 10.3847/2041-8213/aaf96e

2019 doi
[26]

E., & Nichols, D

Flanagan, E. E., & Nichols, D. A. 2017, Phys. Rev. D, 95, 044002, doi: 10.1103/PhysRevD.95.044002

2017 doi
[27]

2025, Phys

Gasparotto, S., Franciolini, G., & Domcke, V. 2025, Phys. Rev. D, 112, 103021, doi: 10.1103/ngfw-dvwz

2025 doi
[28]

2023, Phys

Barausse, E. 2023, Phys. Rev. D, 107, 124033, doi: 10.1103/PhysRevD.107.124033

2023 doi
[29]

E., & Hughes, S

Holz, D. E., & Hughes, S. A. 2005, Astrophys. J., 629, 15, doi: 10.1086/431341 H¨ ubner, M., Talbot, C., Lasky, P. D., & Thrane, E. 2020, Physical Review D, 101, 023011, doi: 10.1103/PhysRevD.101.023011 Inchausp´ e, H., Gasparotto, S., Blas, D., et al. 2025, Phys. Rev. D, 111,...

2005 doi
[30]

2016, JCAP, 05, 059, doi: 10.1088/1475-7516/2016/05/059

Kehagias, A., & Riotto, A. 2016, JCAP, 05, 059, doi: 10.1088/1475-7516/2016/05/059

2016 doi
[31]

2021, Phys

Khera, N., Krishnan, B., Ashtekar, A., & De Lorenzo, T. 2021, Phys. Rev. D, 103, 044012, doi: 10.1103/PhysRevD.103.044012

2021 doi
[32]

D., Thrane, E., Levin, Y., Blackman, J., & Chen, Y

Lasky, P. D., Thrane, E., Levin, Y., Blackman, J., & Chen, Y. 2016, Phys. Rev. Lett., 117, 061102, doi: 10.1103/PhysRevLett.117.061102

2016 doi
[33]

Linder, E. V. 2003, Phys. Rev. Lett., 90, 091301, doi: 10.1103/PhysRevLett.90.091301

2003 doi
[34]

2025, Phys

Lodha, K., et al. 2025, Phys. Rev. D, 112, 083511, doi: 10.1103/w4c6-1r5j

2025 doi
[35]

Ludwick, K. J. 2017, Mod. Phys. Lett. A, 32, 1730025, doi: 10.1142/S0217732317300257

2017 doi
[36]

2007, Gravitational Waves

Maggiore, M. 2007, Gravitational Waves. Vol. 1: Theory and Experiments (Oxford: Oxford University Press), doi: 10.1093/acprof:oso/9780198570745.001.0001

2007
[37]

2025, Class

Mandal, S., & Shankaranarayanan, S. 2025, Class. Quant. Grav., 42, 23LT01, doi: 10.1088/1361-6382/ae2059

2025 doi
[38]

2026, Modified theories of gravity at different curvature scales, doi: 10.1016/b978-0-443-21439-4.00106-1 16

Mandal, S., & Shankaranarayanan, S. 2026, Modified theories of gravity at different curvature scales, doi: 10.1016/b978-0-443-21439-4.00106-1 16

2026 doi
[39]

2024, Annalen Phys., 536, 2200180, doi: 10.1002/andp.202200180

Mastrogiovanni, S., Karathanasis, C., Gair, J., et al. 2024, Annalen Phys., 536, 2200180, doi: 10.1002/andp.202200180

2024 doi
[40]

Sievers, J. L. 2010, Astrophys. J., 725, 496, doi: 10.1088/0004-637X/725/1/496

2010 doi
[41]

2024, gwastro/pycbc: v2.3.3 release of PyCBC, v2.3.3 Zenodo, doi: 10.5281/zenodo.10473621

Nitz, A., Harry, I., Brown, D., et al. 2024, gwastro/pycbc: v2.3.3 release of PyCBC, v2.3.3 Zenodo, doi: 10.5281/zenodo.10473621

2024 doi
[42]

Peebles, P. J. E. 2025, Phil. Trans. Roy. Soc. Lond. A, 383, 20240021, doi: 10.1098/rsta.2024.0021

2025
[43]

2019, Bulletin of the AAS, 51

Perlmutter, S., Aldering, G., Baltay, C., et al. 2019, Bulletin of the AAS, 51

2019
[44]

L., Karwal, T., & Kamionkowski, M

Poulin, V., Smith, T. L., Karwal, T., & Kamionkowski, M. 2019, Phys. Rev. Lett., 122, 221301, doi: 10.1103/PhysRevLett.122.221301

2019 doi
[45]

2020, Phys

Pratten, G., Husa, S., Garcia-Quiros, C., et al. 2020, Phys. Rev. D, 102, 064001, doi: 10.1103/PhysRevD.102.064001

2020 doi
[46]

G., et al

Riess, A. G., et al. 2022, Astrophys. J. Lett., 934, L7, doi: 10.3847/2041-8213/ac5c5b

2022 doi
[47]

Schutz, B. F. 1986, Nature, 323, 310, doi: 10.1038/323310a0

1986 doi
[48]

2020, Proc

Scott, D. 2020, Proc. Int. Sch. Phys. Fermi, 200, 133, doi: 10.3254/ENFI200007

2020 doi
[49]

A., & Sethi, S

Sen, A. A., & Sethi, S. 2002, Phys. Lett. B, 532, 159, doi: 10.1016/S0370-2693(02)01547-2

2002 doi
[50]

Shankaranarayanan, S., & Johnson, J. P. 2022, Gen. Rel. Grav., 54, 44, doi: 10.1007/s10714-022-02927-2

2022 doi
[51]

2019, Bulletin of the AAS, 51

Slosar, A., Mandelbaum, R., & Eisenstein, D. 2019, Bulletin of the AAS, 51

2019
[52]

2019, Astrophys

Soares-Santos, M., et al. 2019, Astrophys. J. Lett., 876, L7, doi: 10.3847/2041-8213/ab14f1

2019 doi
[53]

2014, Journal of High Energy Physics, 2014, doi: 10.1007/jhep07(2014)152

Strominger, A. 2014, Journal of High Energy Physics, 2014, doi: 10.1007/jhep07(2014)152

2014 doi
[54]

2018, Astrophys

Talbot, C., & Thrane, E. 2018, Astrophys. J., 856, 173, doi: 10.3847/1538-4357/aab34c

2018 doi
[55]

2019, Publ

Thrane, E., & Talbot, C. 2019, Publ. Astron. Soc. Austral., 36, e010, doi: 10.1017/pasa.2019.2

2019 doi
[56]

Tolish, A., & Wald, R. M. 2016, Phys. Rev. D, 94, 044009, doi: 10.1103/PhysRevD.94.044009

2016 doi
[57]

2010, Phys

Veitch, J., & Vecchio, A. 2010, Phys. Rev. D, 81, 062003, doi: 10.1103/PhysRevD.81.062003

2010 doi
[58]

2024, Phys

Xu, Y., Rossell´ o-Sastre, M., Tiwari, S., et al. 2024, Phys. Rev. D, 109, 123034, doi: 10.1103/PhysRevD.109.123034

2024 doi

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

2016, Phys

Abbott, B., et al. 2016, Phys. Rev. Lett., 116, 061102, doi: 10.1103/PhysRevLett.116.061102

doi:10.1103/physrevlett.116.061102 2016

[2] [2]

P., et al

Abbott, B. P., et al. 2016, Phys. Rev. Lett., 116, 221101, doi: 10.1103/PhysRevLett.116.221101

doi:10.1103/physrevlett.116.221101 2016

[3] [3]

P., et al

Abbott, B. P., et al. 2017a, Phys. Rev. Lett., 119, 161101, doi: 10.1103/PhysRevLett.119.161101

doi:10.1103/physrevlett.119.161101

[4] [4]

P., et al

Abbott, B. P., et al. 2017b, Nature, 551, 85, doi: 10.1038/nature24471

doi:10.1038/nature24471

[5] [5]

P., et al

Abbott, B. P., et al. 2017c, Astrophys. J. Lett., 848, L12, doi: 10.3847/2041-8213/aa91c9

doi:10.3847/2041-8213/aa91c9

[6] [6]

2023, Phys

Abbott, R., et al. 2023, Phys. Rev. X, 13, 011048, doi: 10.1103/PhysRevX.13.011048

doi:10.1103/physrevx.13.011048 2023

[7] [7]

2022, JHEAp, 34, 49, doi: 10.1016/j.jheap.2022.04.002

Abdalla, E., et al. 2022, JHEAp, 34, 49, doi: 10.1016/j.jheap.2022.04.002

doi:10.1016/j.jheap.2022.04.002 2022

[8] [8]

2020, Astron

Aghanim, N., et al. 2020, Astron. Astrophys., 641, A6, doi: 10.1051/0004-6361/201833910

doi:10.1051/0004-6361/201833910 2020