Identifying Monochromatic Signals in LISA and Taiji via Spectral Split: Gravitational Waves versus Ultralight Dark Matter

Di Chen; Tingyuan Jiang; Wenyan Ren; Yong Tang; Yue-Hui Yao; Yu-Feng Zhou

REVIEW 2 major objections 4 minor 2 cited by

Identifying Monochromatic Signals in LISA and Taiji via Spectral Split: Gravitational Waves versus Ultralight Dark Matter

T0 review · 2 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read The annual orbit of LISA and Taiji splits monochromatic signals into harmonic combs whose width reveals whether they come from gravitational waves or ultralight dark matter.

desk verdict The paper has a genuinely new physical idea and a solid analytic derivation; the abstract oversells it as a ready-made discriminator, but the underlying spectral-split observation is worth publishing. read the letter →

arxiv 2508.14655 v1 pith:SMYYRW4S submitted 2025-08-20 hep-ph astro-ph.COgr-qc

Yue-Hui Yao , Tingyuan Jiang , Wenyan Ren , Di Chen , Yong Tang , Yu-Feng Zhou This is my paper

classification hep-phastro-ph.COgr-qc

keywords ultralightdarkmattergravitationalwavesLISATaijispectralsplitannualmodulationDopplerharmonicsFishermatrix

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

This paper claims that the annual, heliocentric motion of space-based gravitational-wave detectors like LISA and Taiji imprints a spectral fingerprint on every monochromatic signal, splitting it into harmonics spaced by one orbital frequency, and that the number and strength of harmonics differ sharply between gravitational waves and ultralight dark matter. If true, a single loud monochromatic event can be identified as one or the other simply by its harmonic pattern, without relying on detector-channel comparisons that are themselves noise-limited. The authors derive the modulated spectra analytically, confirm them with numerical simulation, and use Fisher-matrix forecasts to show that a ULDM mass could be pinned down to about one part in 10^4. The broader payoff is that ULDM searches can piggyback on ordinary gravitational-wave data analysis rather than requiring a separate experimental program.

What carries the argument

The central object is the modulated response of the Michelson X channel to a monochromatic source. Written as a sum over harmonics of the orbital frequency f_m = 1/yr, the gravitational-wave response (Eq. 5) contains both orbital-orientation coefficients G_p^(n) and Doppler coefficients D^(n) = J_n(ϵ) with ϵ = 2π f r_⊙ sin θ, which spread power to high orders; the ULDM response (Eq. 6) has only the G_p^(n) with n = -2, ..., +2 because the spatial dependence of the field across the orbit is negligible. The contrast in harmonic content is the mechanism that separates the two hypotheses.

What would settle it

Take a detected monochromatic signal in LISA or Taiji and measure the relative power in harmonics spaced by f_m = 1/yr out to |n| ≳ 10. For a gravitational wave at f ≈ 1 mHz, the Doppler parameter ϵ ≈ 2π f r_⊙ sin θ ≈ 0.3 should produce higher-order harmonics with predictable amplitudes; for ULDM at the same Compton frequency they should be absent. A single high-SNR event with a measured harmonic ladder—or a null measurement of high-order harmonics in a candidate ULDM signal—would confirm or refute the mechanism.

Watch

Extended reading notes

Core claim

The central discovery is a spectral split: the detector's orbit modulates both gravitational-wave and ULDM signals, but only the gravitational-wave response contains Doppler harmonics beyond the detector-orientation harmonics. For gravitational waves, the response factorizes into geometric coefficients G_p^(n) with |n| ≤ 4 and Doppler coefficients D^(n) = J_n(ϵ) whose Bessel spread grows with ϵ = 2π f r_⊙ sin θ, so at millihertz frequencies many harmonics carry signal power. For ULDM, the field amplitude is effectively frozen over the orbit (relative change ~6 × 10^-3 at m ~ 10^-17 eV), so there is no Doppler term and only harmonics n = -2, ..., +2 survive. The paper argues that this differe

Load-bearing premise

The clean spectral separation assumes the ULDM field amplitude is effectively constant over the detector's orbit, so no Doppler modulation appears; this holds while the orbit is much smaller than the field coherence length (about 0.6% amplitude change at 10^-17 eV), and the paper does not quantify the mass range where the assumption, and thus the distinction, breaks down.

Editorial extensions

If this is right

A monochromatic signal's harmonic ladder—spacing fixed at ~1/yr, width set by the Doppler parameter ϵ—directly identifies whether it came from a compact-binary gravitational wave or ULDM, without needing multi-channel comparisons.
For a gravitational-wave signal with SNR 10 in the paper's example, matched filtering with ULDM templates captures at most SNR ~5.4, so the correct template wins by roughly a factor of two in SNR.
For a genuine ULDM signal, gravitational-wave templates cannot explain the absence of high-order harmonics except as noise fluctuations, suppressing the chance of misclassification.
ULDM mass can be measured to a relative precision of about 10^-4 for an SNR ~6 signal in a four-year LISA observation, while the direction of the ULDM field's polarization ellipse is poorly constrained because the angular resolution is set by the coherence length, about 10^3 times worse than for gravitational waves.
The analytical spectra agree with numerical simulations that drop the rigid adiabatic approximation, indicating the harmonic structure is not an artifact of that approximation; a full Bayesian analysis with detector noise is still needed to turn the spectral difference into a formal model-selection statement.

Reading between the lines

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

The same harmonic-split logic should transfer to any detector whose motion modulates the signal; for a geocentric mission the Earth's annual orbit would set the same ~1/yr spacing, so the method is not intrinsically tied to heliocentric LISA/Taiji configurations.
The clean separation is expected to weaken for ULDM masses above roughly 10^-16 eV, where the coherence length approaches the orbital radius and the frozen-amplitude assumption fails; identifying the exact threshold is a natural follow-up.
The claimed SNR contrast is computed for a specific parameter example; a full template-bank search over the seven-parameter signal space could change the effective detection significance, so the practical gain should be re-evaluated with Bayesian model selection.

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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

Colleague – this one is worth a look. The new thing is the observation that ULDM, because its coherence length is enormous, does not get Doppler-modulated by the detector's orbit, while GWs do. So in LISA/Taiji, a monochromatic source of either type shows a harmonic comb at the orbital frequency, but GWs have a rich set of high-order sidebands (Doppler plus orientation harmonics up to n=±4) whereas ULDM shows only the orientation harmonics n=±2. That is a physical distinction that I don't think is in the previous literature; prior discrimination used different TDI channels.

The derivation is careful. They write the X-channel response starting from first principles, use the rigid-adiabatic plus small-antenna approximation, and give explicit tables of the geometric coefficients. Appendix E validates the analytic spectra against a time-domain numerical simulation that solves the light-propagation delay without the approximation. The agreement in Fig. 5 is real. So the core result—the template-level spectral split—is solid.

Where it gets soft: the abstract says the spectral pattern 'would enable to clearly identify the nature of the signal.' That is a step too far. The paper shows the templates are different, and gives a semi-quantitative example for one parameter set (a GW with SNR 10 yields <5.4 SNR with ULDM templates). But that's not a detection statistic. The distinguishing high harmonics (n=±3, ±4, and Doppler sidebands beyond n=±2) are small at low frequency: at 0.1 mHz, ϵ≲0.3, so those lines sit at 1–8% of the carrier. At the SNR~few that galactic white-dwarf binaries actually have, those lines are plausibly below noise. The paper's conclusion admits that a full Bayesian model-selection analysis is needed; that sentence should have been in the abstract.

The second soft spot is the ULDM constant-amplitude approximation. The 6×10−3 estimate at 10−17 eV is fine, but the paper doesn't say at which mass the coherence length shrinks enough that Doppler modulation returns and the clean split degrades. That's a missing boundary on the claimed method.

The Fisher forecasts assume several parameters are known (inclination/polarization/phase for GW; eccentricity/angle/phase for ULDM), so the 10−4 mass precision is optimistic, though Fisher matrices are always that way.

Bottom line: this is a solid, competent paper with a genuinely new observation. The central physical idea holds; the overclaim is in the presentation. Send it to review, and ask the authors to either add a model-selection calculation or weaken the abstract's claims. I would cite it—it gives a clean, analytically derived prediction that future LISA/Taiji data analysis can test.

Referee Report

2 major / 4 minor

Summary. This paper analyzes how the heliocentric orbital motion of LISA/Taiji modulates monochromatic signals in the X channel. Using analytic Keplerian orbits and the rigid-adiabatic/small-antenna approximations, the authors derive the detector response to a monochromatic GW (Eq. 5) and to vector/scalar ULDM (Eq. 6). The annual motion splits each monochromatic line into harmonics separated by f_m = 1/yr. For GWs the harmonic series is extended by orientation coefficients up to n=±4 and by Doppler Bessel coefficients; for ULDM only n=0,±1,±2 appear because the field amplitude is approximately constant over the detector orbit. This spectral split is proposed as a way to distinguish GW from ULDM monochromatic signals. The authors validate the analytic spectra against a time-domain numerical simulation (Appendix E) and use the Fisher matrix to estimate parameter uncertainties, reporting precise mass measurements for ULDM and source localization for GWs.

Significance. If correct, the spectral-split observable is a genuinely new discriminant for the astrophysical versus dark-matter origin of a monochromatic line in space-based interferometers. The paper's analytic response functions are derived from first principles with clearly stated approximations, and the numerical validation in Appendix E is a notable strength. The spectral split contains no free parameters or fitting, and the Fisher analysis illustrates the potential of the method. However, the central identification claim is supported only by a semi-quantitative SNR comparison for one benchmark; the discriminating power is not yet demonstrated with a detection statistic. The parameter estimation also assumes several parameters known, so the quoted uncertainties are optimistic.

major comments (2)

[§III, Fig. 2, Conclusion] The paper's central claim that the harmonic structure 'would enable to clearly identify the nature of the signal' (Abstract) is not backed by a detection statistic. The only quantitative discrimination evidence is the example in §III where, for a GW signal with SNR=10 at f=1 mHz, a ULDM-template match has SNR<5.4. No details are given for how this SNR is computed (template bank, noise PSD, parameter ranges), and no false-alarm or model-selection probability is provided. At f~0.1 mHz, ϵ≲0.3, and the n=±3,±4 orientation harmonics have amplitudes ~0.01–0.08 relative to the carrier (Table I), so at the SNR~few typical of white-dwarf binaries they are likely buried in noise. The Conclusion explicitly defers a full Bayesian analysis; thus the 'harmonic count alone distinguishes' claim overstates what is demonstrated. A quantitative matched-filter/Bayesian model-selection calculation, or a sign
[Appendix C, Eq. (6)] The discriminator relies on the absence of Doppler modulation in the ULDM signal. This follows from treating a_p(x_1) as constant over the orbit; the authors verify |Δa_p/a_p|~2πr⊙/λ_c≈6×10^-3 only for m~10^-17 eV. The paper does not quantify the mass/frequency range over which this approximation holds. Since λ_c=c/(f_c σ), the ratio grows linearly with f_c: at f_c=10 mHz it is already ~3×10^-2, and near the upper edge of the LISA band it becomes ~0.1–0.3, where the ULDM signal would acquire a Doppler harmonic structure that can mimic the GW spectral split. The validity domain of the spectral discrimination must be stated explicitly, along with the impact of the breakdown on the claimed distinction.

minor comments (4)

[§IV, Fig. 3 caption] The caption for panel (a) reports SNR ≈ 4.2, while the text states SNR ≈ 8.68 for the same system. Please reconcile this discrepancy.
[§IV] Typographical issues: 'the angels θ and ϕ' should be 'the angles θ and ϕ'; 'much worser' should be 'much worse'.
[§III] The phrase 'observing the corresponding spectral pattern directly reveal the signal origin' has a subject-verb disagreement; also 'significant higher-order harmonics than' should be 'significant higher-order harmonics than in'.
[§III] The statement that the GW spectrum includes significant higher-order harmonics would benefit from a quantitative measure, e.g., the cumulative power fraction in harmonics beyond |n|=2 as a function of f and source location, especially since the higher-harmonic amplitudes depend on θ, ϕ, and ϵ.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the harmonic split is derived from first-principles response functions, and self-citations are contextual rather than load-bearing.

full rationale

The paper's central claim is that heliocentric motion splits a monochromatic signal into harmonics, with distinguishable harmonic structure between GWs and ULDM. This is derived analytically from the detector response equations (Eqs. 1, 3, and 4) via Fourier/Bessel expansions, not from fitting or from an assumed conclusion. The GW spectrum in Eq. (5) follows from substituting the response function and expanding the Doppler phase with the Jacobi-Anger identity (Eq. B12); the ULDM spectrum in Eq. (6) follows from the linear coupling in Eq. (3) and the constant-amplitude approximation justified by the small ratio 2πr⊙/λc. The distinction in harmonic content is therefore a consequence of the differing coupling structures and the neglect of Doppler modulation for ULDM, with the latter explicitly quantified as a physical assumption. The Fisher matrix analysis is a theoretical forecast on synthetic signals, not a fit to observed data. Self-citations to Refs. [38,50] are used to motivate the problem and cite earlier sensitivity studies, but they are not the basis for the spectral-split derivation; the numerical simulations in Appendix E independently validate the analytic expressions. The conclusion explicitly states that a full Bayesian analysis is still needed, which is a limitation of scope rather than a circularity. No step reduces by definition to an assumed result, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard signal-response physics plus a few modeling choices: the rigid adiabatic approximation, the small-antenna limit, the nonrelativistic DM halo model, and crucially the assumption that the ULDM field is coherent across the detector orbit. No free parameters are fitted; the Fisher forecasts use chosen source parameters but those are not part of the derivation.

assumptions (5)

domain assumption Rigid adiabatic approximation: arm lengths constant and equal to fiducial L
Invoked in Appendix A and used to derive Eqs. (5) and (6); validated numerically in Appendix E, so its failure would affect the harmonic amplitudes.
domain assumption Small-antenna limit δ=2πfL/c ≪ 1
Used in Appendix B (Eq. B10) to keep leading order 4δ^2 in GW response and in Appendix C (Eq. C9) to drop velocity-dependent ULDM terms; at f=10 mHz, δ≈0.5, next-order corrections could matter.
domain assumption ULDM field is coherent over the detector orbit (Doppler modulation absent)
Appendix C: |Δa_p/a_p| ~ 2πr⊙/λc ≈ 6e-3 for m=1e-17 eV; this is the key premise separating ULDM and GW spectra and degrades with increasing ULDM mass.
domain assumption Nonrelativistic DM velocity distribution with σ~1e-3
Sec II and App E assume σ~1e-3 and a Maxwellian distribution for coherence scales and simulations.
domain assumption ULDM coupling to test masses via baryon number or B-L (vector) and trace of energy-momentum (scalar)
The signal model in Eq. (3) assumes these dominant couplings; other couplings (e.g., to laser phase) could alter the response.

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Pith. "Pith review of Identifying Monochromatic Signals in LISA and Taiji via Spectral Split: Gravitational Waves versus Ultralight Dark Matter." pith.science (2026). https://pith.science/paper/SMYYRW4S

@misc{pith2026250814655,
  author       = {Pith},
  title        = {Pith review of: Identifying Monochromatic Signals in LISA and Taiji via Spectral Split: Gravitational Waves versus Ultralight Dark Matter},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SMYYRW4S}},
  note         = {Machine review of arXiv:2508.14655}
}

read the original abstract

The detection of gravitational waves (GWs) has opened a new window to explore the dark Universe. Ultralight dark matter (ULDM), an attractive candidate for dark matter, might induce monochromatic signals in gravitational-wave (GW) laser interferometers. However it is not clear how such signals are disentangled from the GWs emitted by galactic compact binaries. Here we initiate the investigation on the spectral split of monochromatic signals caused by detector's heliocentric motion in space and show the annual modulation can induce distinct structures in the spectral harmonics for GWs and ULDM, which would enable to clearly identify the nature of the signal. We show the physical parameters can be inferred with high precision using the Fisher matrix formalism. Our results provide a practical algorithm for probing ULDM and broaden the scientific objectives of future GW detectors in space, such as LISA and Taiji.

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Forward citations

Cited by 2 Pith papers

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Reference graph

Works this paper leans on

76 extracted references · 41 canonical work pages · cited by 2 Pith papers

[1]

hp(t) denotes the time-domain GW waveforms, which is related to that in the radiation frame by h× ± ih+ = e∓2iψ(hrad × ± ihrad + ) with ψ the polarization angle

Monochromatic GWs A GW tensor can be decomposed into the two polar- ization modes [68]: h(t) = hp(t)ep(ˆk), (B1) where the polarization tensors in the solar system barycenter (SSB) frame are defined as e+ = ˆu ⊗ ˆu − ˆv ⊗ ˆv, e× = ˆu ⊗ ˆv + ˆv ⊗ ˆu, (B2) where, ˆk = −[cos ϕ sin θ, sin ϕ sin θ, cos θ] is the unit wave vector for a source located at polar a...

work page
[2]

Since the data channels (e.g

Response to GWs We now derive the signal induced by a monochro- matic GW in interferometers. Since the data channels (e.g. Eq. (4)) are constructed from the single-link data streams, we first investigate the response of a single laser link to the GW. Substituting Eqs. (B1) and (B4) into Eq. (1), we have yrs(t) = ei2πf t X p=+,× Rp rs(f, ˆk)Hp, (B5) where ...

work page
[3]

Each plane wave has a random amplitude βv,p drawn independently from the Rayleigh distribu- tion with unit scale parameter, and a random phase φv,p drawn uniformly over [0, 2π)

Stochastic ULDM The ULDM field is modeled as a superposition of plane waves, each representing the collective behavior of ULDM particles residing in the same volume of phase space [40, 43, 58–60]: A(x) = A0 X p ˆxp X v βv,p p ∆(v)ei(ωt−k·x+φv,p), (C1) where ω ≃ m(1 + |v|2/2), k ≃ mv, A0 is a normal- ization constant fixed by the local DM energy density, ∆...

work page
[4]

Using Eq

Response to ULDM Since the field is a superposition of plane waves, the overall signal is the sum of contributions from each plane wave. Using Eq. (3), we find the contribution from a plane wave is given by yrs(t) = ei2πf tX p Rp rs(f, v)Ap, (C4) 8 TABLE I. Geometric coefficients for GWs with the analytical Keplerian orbits. The orbital parameters κ and λ...

work page
[5]

Wilczek, Problem of strong p and t invariance in the presence of instantons, Phys

F. Wilczek, Problem of strong p and t invariance in the presence of instantons, Phys. Rev. Lett. 40, 279 (1978)

work page 1978
[6]

(C1): A(x) = A0 X p ˆxp X v βv,p p ∆(v)ei(ωt−k·x+φv,p)

ULDM field The basic expression used in our ULDM field simula- tion is Eq. (C1): A(x) = A0 X p ˆxp X v βv,p p ∆(v)ei(ωt−k·x+φv,p). We outline two general considerations underlying the simulation. First, while the velocity distribution of DM is continuous, only a finite number of points can be sampled in momentum space on a computer. There- fore, we carry ...

work page
[7]

The equation can be solved perturbatively in powers of ε = RS/2r⊙ ∼ 10−8 [69], where RS = 2GM⊙ is the Schwarzschild radius of the Sun, Lrs ≃ L(0) rs + L(1/2) rs + O(ε1)

Moving detector In modeling the detector motion, the key step is to solve the transcendental light propagation equation t − ts = |xr(t) − xs(ts)|, which determines the light travel time Lrs = t − ts between spacecraft. The equation can be solved perturbatively in powers of ε = RS/2r⊙ ∼ 10−8 [69], where RS = 2GM⊙ is the Schwarzschild radius of the Sun, Lrs...

work page
[8]

Cirelli, A

M. Cirelli, A. Strumia, and J. Zupan, Dark matter (2024), arXiv:2406.01705 [hep-ph]

arXiv 2024

Show all 76 references

[9]

Chadha-Day, J

F. Chadha-Day, J. Ellis, and D. J. E. Marsh, Axion dark matter: What is it and why now?, Sci. Adv. 8, abj3618 12 (2022), arXiv:2105.01406 [hep-ph]

2022 arXiv
[10]

R. D. Peccei and H. R. Quinn, CP conservation in the presence of pseudoparticles, Phys. Rev. Lett. 38, 1440 (1977)

1977
[11]

Weinberg, A new light boson?, Phys

S. Weinberg, A new light boson?, Phys. Rev. Lett. 40, 223 (1978)

1978
[12]

P. W. Graham, J. Mardon, and S. Rajendran, Vector dark matter from inflationary fluctuations, Phys. Rev. D 93, 103520 (2016)

2016
[13]

The velocity-dependent terms in Eq

For the analytical Keplerian orbits given in Appendix A, we find Gp(t) = 2X n=−2 G(n) p ei2πnfmt, (C10) where the coefficients G(n) p are listed in Table II. The velocity-dependent terms in Eq. (C9) represent the con- tribution of the field gradient and only become impor- tant...
[14]

Preskill, M

J. Preskill, M. B. Wise, and F. Wilczek, Cosmology of the invisible axion, Physics Letters B 120, 127 (1983)

1983
[15]

Dine and W

M. Dine and W. Fischler, The Not So Harmless Axion, Phys. Lett. B 120, 137 (1983)

1983
[16]

Damour and A

T. Damour and A. M. Polyakov, String theory and gravity, Gen. Rel. Grav. 26, 1171 (1994), arXiv:gr- qc/9411069

1994
[17]

Damour and A

T. Damour and A. M. Polyakov, The String dilaton and a least coupling principle, Nucl. Phys. B 423, 532 (1994), arXiv:hep-th/9401069

1994 arXiv
[18]

Capozziello and M

S. Capozziello and M. De Laurentis, Extended Theories of Gravity, Phys. Rept. 509, 167 (2011), arXiv:1108.6266 [gr-qc]

2011 arXiv
[19]

A. E. Nelson and J. Scholtz, Dark light, dark matter, and the misalignment mechanism, Phys. Rev. D 84, 103501 (2011)

2011
[20]

Y. Ema, K. Nakayama, and Y. Tang, Production of purely gravitational dark matter: the case of fermion and vector boson, JHEP 07, 060, arXiv:1903.10973 [hep-ph]

1903 arXiv
[21]

L. Hui, J. P. Ostriker, S. Tremaine, and E. Witten, Ul- tralight scalars as cosmological dark matter, Phys. Rev. D 95, 043541 (2017)

2017
[22]

Hui, Wave dark matter, Annual Review of Astronomy and Astrophysics 59, 247 (2021)

L. Hui, Wave dark matter, Annual Review of Astronomy and Astrophysics 59, 247 (2021)

2021
[23]

Schive, T

H.-Y. Schive, T. Chiueh, and T. Broadhurst, Cos- mic Structure as the Quantum Interference of a Co- herent Dark Wave, Nature Phys. 10, 496 (2014), arXiv:1406.6586 [astro-ph.GA]

2014 arXiv
[24]

G. P. Centers et al., Stochastic fluctuations of bosonic dark matter, Nature Commun. 12, 7321 (2021), arXiv:1905.13650 [astro-ph.CO]

2021 arXiv
[25]

S. M. Vermeulen et al., Direct limits for scalar field dark matter from a gravitational-wave detector, Nature 600, 424–428 (2021), arXiv:2103.03783 [gr-qc]

2021 arXiv
[26]

Y. Chen, Y. Liu, R.-S. Lu, Y. Mizuno, J. Shu, X. Xue, Q. Yuan, and Y. Zhao, Stringent axion constraints with Event Horizon Telescope polarimetric measurements of M87⋆, Nature Astron. 6, 592 (2022), arXiv:2105.04572 [hep-ph]

2022 arXiv
[27]

Gavilan-Martin et al., Searching for dark matter with a spin-based interferometer, Nature Commun

D. Gavilan-Martin et al., Searching for dark matter with a spin-based interferometer, Nature Commun. 16, 4953 (2025), arXiv:2408.02668 [hep-ph]

2025
[28]

Y.-D. Tsai, J. Eby, and M. S. Safronova, Direct detec- tion of ultralight dark matter bound to the Sun with space quantum sensors, Nature Astron. 7, 113 (2023), arXiv:2112.07674 [hep-ph]

2023 arXiv
[29]

H. An, X. Chen, S. Ge, J. Liu, and Y. Luo, Searching for ultralight dark matter conversion in solar corona using Low Frequency Array data, Nature Commun. 15, 915 (2024), arXiv:2301.03622 [hep-ph]

2024 arXiv
[30]

Jiang et al., Search for dark photons with synchro- nized quantum sensor network, Nature Commun

M. Jiang et al., Search for dark photons with synchro- nized quantum sensor network, Nature Commun. 15, 3331 (2024), arXiv:2305.00890 [quant-ph]

2024 arXiv
[31]

P. Du, D. Egana-Ugrinovic, R. Essig, G. Fragione, and R. Perna, Searching for ultra-light bosons and con- straining black hole spin distributions with stellar tidal disruption events, Nature Commun. 13, 4626 (2022), arXiv:2202.01215 [hep-ph]

2022 arXiv
[32]

D. Blas, S. Gasparotto, and R. Vicente, Searching for ultralight dark matter through frequency modulation of gravitational waves, Phys. Rev. D 111, 042008 (2025)

2025
[33]

Khmelnitsky and V

A. Khmelnitsky and V. Rubakov, Pulsar timing sig- nal from ultralight scalar dark matter, JCAP 02, 019, arXiv:1309.5888 [astro-ph.CO]

arXiv
[34]

T. Liu, X. Lou, and J. Ren, Pulsar Polarization Arrays, Phys. Rev. Lett. 130, 121401 (2023), arXiv:2111.10615 [astro-ph.HE]

2023 arXiv
[35]

J. S. Bullock and M. Boylan-Kolchin, Small-Scale Chal- lenges to the ΛCDM Paradigm, Ann. Rev. Astron. As- trophys. 55, 343 (2017), arXiv:1707.04256 [astro-ph.CO]

2017 arXiv
[36]

W. J. G. de Blok, The Core-Cusp Problem, Adv. Astron. 2010, 789293 (2010), arXiv:0910.3538 [astro-ph.CO]

2010 arXiv
[37]

Boylan-Kolchin, J

M. Boylan-Kolchin, J. S. Bullock, and M. Kaplinghat, Too big to fail? The puzzling darkness of massive Milky Way subhaloes, Mon. Not. Roy. Astron. Soc. 415, L40 (2011), arXiv:1103.0007 [astro-ph.CO]

2011 arXiv
[38]

Tulin and H.-B

S. Tulin and H.-B. Yu, Dark Matter Self-interactions and Small Scale Structure, Phys. Rept. 730, 1 (2018), arXiv:1705.02358 [hep-ph]

2018 arXiv
[39]

B. P. Abbott et al.(LIGO Scientific, Virgo), Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116, 061102 (2016), arXiv:1602.03837 [gr-qc]

2016 arXiv
[40]

Pierce, K

A. Pierce, K. Riles, and Y. Zhao, Searching for dark pho- ton dark matter with gravitational-wave detectors, Phys. Rev. Lett. 121, 061102 (2018)

2018
[41]

Morisaki and T

S. Morisaki and T. Suyama, Detectability of ultralight scalar field dark matter with gravitational-wave detec- tors, Phys. Rev. D 100, 123512 (2019)

2019
[42]

Grote and Y

H. Grote and Y. V. Stadnik, Novel signatures of dark matter in laser-interferometric gravitational-wave detec- tors, Phys. Rev. Res. 1, 033187 (2019)

2019
[43]

H.-K. Guo, K. Riles, F.-W. Yang, and Y. Zhao, Searching for Dark Photon Dark Matter in LIGO O1 Data, Com- mun. Phys. 2, 155 (2019), arXiv:1905.04316 [hep-ph]

2019 arXiv
[44]

A. L. Miller and L. Mendes, First search for ultralight dark matter with a space-based gravitational-wave an- tenna: Lisa pathfinder, Phys. Rev. D 107, 063015 (2023)

2023
[45]

Yu, Y.-H

J.-C. Yu, Y.-H. Yao, Y. Tang, and Y.-L. Wu, Sensitiv- ity of space-based gravitational-wave interferometers to ultralight bosonic fields and dark matter, Phys. Rev. D 108, 083007 (2023)

2023
[46]

Fukusumi, S

K. Fukusumi, S. Morisaki, and T. Suyama, Upper limit on scalar field dark matter from ligo-virgo third observa- tion run, Phys. Rev. D 108, 095054 (2023)

2023
[47]

Kim, Gravitational interaction of ultralight dark matter with interferometers, JCAP 12, 018, arXiv:2306.13348 [hep-ph]

H. Kim, Gravitational interaction of ultralight dark matter with interferometers, JCAP 12, 018, arXiv:2306.13348 [hep-ph]

arXiv
[48]

Manita, H

Y. Manita, H. Takeda, K. Aoki, T. Fujita, and S. Muko- hyama, Exploring the spin of ultralight dark matter with gravitational wave detectors, Phys. Rev. D 109, 095012 (2024)

2024
[49]

J.-C. Yu, Y. Cao, Y. Tang, and Y.-L. Wu, Detecting ul- tralight dark matter gravitationally with laser interfer- ometers in space, Phys. Rev. D 110, 023025 (2024)

2024
[50]

Yao and Y

Y.-H. Yao and Y. Tang, Probing stochastic ultralight dark matter with space-based gravitational-wave inter- 13 ferometers, Phys. Rev. D 110, 095015 (2024)

2024
[51]

Gu´ e, A

J. Gu´ e, A. Hees, and P. Wolf, Probing the axion photon coupling with space-based gravitational wave detectors, Class. Quant. Grav. 42, 055015 (2025), arXiv:2410.17763 [hep-ph]

2025 arXiv
[52]

Y.-H. Yao, T. Jiang, and Y. Tang, Prospects for axion dark matter searches at lisa-like interferometers, Phys. Rev. D 111, 055031 (2025)

2025
[53]

Yao, X.-J

R.-M. Yao, X.-J. Bi, P.-F. Yin, and Q.-G. Huang, Axion- like dark matter search with space-based gravitational wave detectors (2025), arXiv:2504.10083 [hep-ph]

2025
[54]

Zhang, J

J.-R. Zhang, J. Chen, H.-S. Jiao, R.-G. Cai, and Y.-L. Zhang, Probing spin-2 ultralight dark matter with space- based gravitational wave detectors in millihertz (2025), arXiv:2501.11071 [gr-qc]

2025
[55]

A. L. Miller, Gravitational wave probes of particle dark matter: a review (2025), arXiv:2503.02607 [astro-ph.HE]

2025
[56]

D. W. P. Amaral, M. Jain, M. A. Amin, and C. Tunnell, Vector wave dark matter and terrestrial quantum sensors, JCAP 06, 050, arXiv:2403.02381 [hep-ph]

arXiv
[57]

Xu, Y.-H

H.-T. Xu, Y.-H. Yao, Y. Tang, and Y.-L. Wu, Distin- guishing monochromatic signals in lisa and taiji: Ul- tralight dark matter versus gravitational waves (2025), arXiv:2506.09744 [hep-ph]

2025 arXiv
[58]

P. A.-S. et al, Laser interferometer space antenna (2017), arXiv:1702.00786 [astro-ph.IM]

2017 arXiv
[59]

Hu and Y.-L

W.-R. Hu and Y.-L. Wu, The Taiji Program in Space for gravitational wave physics and the nature of gravity, Natl. Sci. Rev. 4, 685 (2017)

2017
[60]

Luo, L.-S

J. Luo, L.-S. Chen, H.-Z. Duan, Y.-G. Gong, S. Hu, J. Ji, Q. Liu, J. Mei, V. Milyukov, M. Sazhin, C.-G. Shao, V. T. Toth, H.-B. Tu, Y. Wang, Y. Wang, H.-C. Yeh, M.-S. Zhan, Y. Zhang, V. Zharov, and Z.-B. Zhou, Tianqin: a space-borne gravitational wave detector, Classical and Q...

2016
[61]

J. D. Romano and N. J. Cornish, Detection meth- ods for stochastic gravitational-wave backgrounds: a unified treatment, Living Rev. Rel. 20, 2 (2017), arXiv:1608.06889 [gr-qc]

2017 arXiv
[62]

Babak, M

S. Babak, M. Hewitson, and A. Petiteau, Lisa sensitiv- ity and snr calculations (2021), arXiv:2108.01167 [astro- ph.IM]

2021 arXiv
[63]

J. D. Romano and B. Allen, Answers to frequently asked questions about the pulsar timing array hellings and downs curve, Classical and Quantum Gravity 41, 175008 (2024)

2024
[64]

Freese, M

K. Freese, M. Lisanti, and C. Savage, Colloquium: An- nual modulation of dark matter, Rev. Mod. Phys. 85, 1561 (2013), arXiv:1209.3339 [astro-ph.CO]

2013 arXiv
[65]

Derevianko, Detecting dark-matter waves with a net- work of precision-measurement tools, Phys

A. Derevianko, Detecting dark-matter waves with a net- work of precision-measurement tools, Phys. Rev. A 97, 042506 (2018)

2018
[66]

J. W. Foster, N. L. Rodd, and B. R. Safdi, Revealing the dark matter halo with axion direct detection, Phys. Rev. D 97, 123006 (2018)

2018
[67]

D. Y. Cheong, N. L. Rodd, and L.-T. Wang, Quantum de- scription of wave dark matter, Phys. Rev. D 111, 015028 (2025)

2025
[68]

F. B. Estabrook, M. Tinto, and J. W. Armstrong, Time- delay analysis of lisa gravitational wave data: Elimina- tion of spacecraft motion effects, Phys. Rev. D62, 042002 (2000)

2000
[69]

S. V. Dhurandhar, K. R. Nayak, and J.-Y. Vinet, Alge- braic approach to time-delay data analysis for lisa, Phys. Rev. D 65, 102002 (2002)

2002
[70]

Vallisneri, Geometric time delay interferometry, Phys

M. Vallisneri, Geometric time delay interferometry, Phys. Rev. D 72, 042003 (2005)

2005
[71]

Tinto and S

M. Tinto and S. V. Dhurandhar, Time-delay interferom- etry, Living Rev. Rel. 24, 1 (2021)

2021
[72]

L. J. Rubbo, N. J. Cornish, and O. Poujade, Forward modeling of space-borne gravitational wave detectors, Phys. Rev. D 69, 082003 (2004)

2004
[73]

Vallisneri, Use and abuse of the fisher information ma- trix in the assessment of gravitational-wave parameter- estimation prospects, Phys

M. Vallisneri, Use and abuse of the fisher information ma- trix in the assessment of gravitational-wave parameter- estimation prospects, Phys. Rev. D 77, 042001 (2008)

2008
[74]

Gu´ e, P

J. Gu´ e, P. Wolf, and A. Hees, Discriminating scalar ul- tralight dark matter from quasi-monochromatic gravita- tional waves in LISA, (2025), arXiv:2508.13847 [gr-qc]

2025 arXiv
[75]

Maggiore, Gravitational Waves

M. Maggiore, Gravitational Waves. Vol. 1: Theory and Experiments (Oxford University Press, 2007)

2007
[76]

Chauvineau, T

B. Chauvineau, T. Regimbau, J.-Y. Vinet, and S. Pireaux, Relativistic analysis of the lisa long range optical links, Phys. Rev. D 72, 122003 (2005)

2005

Pith tools

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

[1] [1]

hp(t) denotes the time-domain GW waveforms, which is related to that in the radiation frame by h× ± ih+ = e∓2iψ(hrad × ± ihrad + ) with ψ the polarization angle

Monochromatic GWs A GW tensor can be decomposed into the two polar- ization modes [68]: h(t) = hp(t)ep(ˆk), (B1) where the polarization tensors in the solar system barycenter (SSB) frame are defined as e+ = ˆu ⊗ ˆu − ˆv ⊗ ˆv, e× = ˆu ⊗ ˆv + ˆv ⊗ ˆu, (B2) where, ˆk = −[cos ϕ sin θ, sin ϕ sin θ, cos θ] is the unit wave vector for a source located at polar a...

work page

[2] [2]

Since the data channels (e.g

Response to GWs We now derive the signal induced by a monochro- matic GW in interferometers. Since the data channels (e.g. Eq. (4)) are constructed from the single-link data streams, we first investigate the response of a single laser link to the GW. Substituting Eqs. (B1) and (B4) into Eq. (1), we have yrs(t) = ei2πf t X p=+,× Rp rs(f, ˆk)Hp, (B5) where ...

work page

[3] [3]

Each plane wave has a random amplitude βv,p drawn independently from the Rayleigh distribu- tion with unit scale parameter, and a random phase φv,p drawn uniformly over [0, 2π)

Stochastic ULDM The ULDM field is modeled as a superposition of plane waves, each representing the collective behavior of ULDM particles residing in the same volume of phase space [40, 43, 58–60]: A(x) = A0 X p ˆxp X v βv,p p ∆(v)ei(ωt−k·x+φv,p), (C1) where ω ≃ m(1 + |v|2/2), k ≃ mv, A0 is a normal- ization constant fixed by the local DM energy density, ∆...

work page

[4] [4]

Using Eq

Response to ULDM Since the field is a superposition of plane waves, the overall signal is the sum of contributions from each plane wave. Using Eq. (3), we find the contribution from a plane wave is given by yrs(t) = ei2πf tX p Rp rs(f, v)Ap, (C4) 8 TABLE I. Geometric coefficients for GWs with the analytical Keplerian orbits. The orbital parameters κ and λ...

work page

[5] [5]

Wilczek, Problem of strong p and t invariance in the presence of instantons, Phys

F. Wilczek, Problem of strong p and t invariance in the presence of instantons, Phys. Rev. Lett. 40, 279 (1978)

work page 1978

[6] [6]

(C1): A(x) = A0 X p ˆxp X v βv,p p ∆(v)ei(ωt−k·x+φv,p)

ULDM field The basic expression used in our ULDM field simula- tion is Eq. (C1): A(x) = A0 X p ˆxp X v βv,p p ∆(v)ei(ωt−k·x+φv,p). We outline two general considerations underlying the simulation. First, while the velocity distribution of DM is continuous, only a finite number of points can be sampled in momentum space on a computer. There- fore, we carry ...

work page

[7] [7]

The equation can be solved perturbatively in powers of ε = RS/2r⊙ ∼ 10−8 [69], where RS = 2GM⊙ is the Schwarzschild radius of the Sun, Lrs ≃ L(0) rs + L(1/2) rs + O(ε1)

Moving detector In modeling the detector motion, the key step is to solve the transcendental light propagation equation t − ts = |xr(t) − xs(ts)|, which determines the light travel time Lrs = t − ts between spacecraft. The equation can be solved perturbatively in powers of ε = RS/2r⊙ ∼ 10−8 [69], where RS = 2GM⊙ is the Schwarzschild radius of the Sun, Lrs...

work page

[8] [8]

Cirelli, A

M. Cirelli, A. Strumia, and J. Zupan, Dark matter (2024), arXiv:2406.01705 [hep-ph]

arXiv 2024