Detecting a gravitational-wave background with next-generation space interferometers

Atsushi Taruya; Hideaki Kudoh; Takashi Hiramatsu; Yoshiaki Himemoto

REVIEW

Detecting a gravitational-wave background with next-generation space interferometers

Hideaki Kudoh, Atsushi Taruya, Takashi Hiramatsu, Yoshiaki Himemoto

General Relativity and Quantum Cosmology · Submitted 27 Nov 2005 · 41 references

Pith's verdict: A careful, honest extension of the Allen–Romano optimal filter to complex overlap reduction functions, wrapped around sensitivity forecasts whose headline numbers are openly conditional on foreground modeling the authors do not resolve.

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CitationAtsushi Taruya, Hideaki Kudoh, Takashi Hiramatsu, Yoshiaki Himemoto. "Detecting a gravitational-wave background with next-generation space interferometers." arXiv:gr-qc/0511145 (2005). https://pith.science/paper/AQTU4U6E

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Editor's note

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Two things worth your time here. First, Eqs. (21)–(25) generalize the Allen–Romano optimal filter to the case where the overlap reduction function is complex, which is what happens for Doppler-tracking readouts on space interferometers. That is a real extension, not a restatement, and the derivation is clean: Appendix A does the Wick expansion term by term, footnote 2 gives the positive-definiteness argument for the cross-correlation variance, and Appendix C handles the noise-only terms that a naive substitution into the orbital average would silently drop. Second, the anisotropic variance in Appendix A.2 is checked numerically rather than asserted — Fig. 6 shows the different-time correlation decaying on the T_* timescale, which is what justifies the delta-function approximation. That is the kind of thing people usually wave at. They don't wave at it here. The dipole numbers in Eqs. (38)–(39) are a straightforward application of Allen–Ottewill and are labeled as such, which is correct scoping. The forecast numbers are the soft part, and the authors know it. Imposing f_cut = 0.2 Hz moves the TDI-DECIGO/BBO limit from 6.8e-18 to 5.8e-15 and flips the ranking against FP-DECIGO. Fig. 3 shows this plainly, and Sec. IV.B says point-source subtraction 'must be clarified.' The stress-test's point lands: the abstract's caveat covers point sources, not the unresolved confusion noise from ref. [34] that the paper itself raises and never quantifies. Since the integrand is dominated by the lowest frequencies in band, a residual floor extending to 0.5–1 Hz would degrade the reach further and could erase the FP-DECIGO advantage. But note the authors hedge this themselves — Sec. IV.B explicitly says it is 'premature to conclude' that 0.5–5 Hz is the best window. So this is a disclosed open problem, not a hidden one, and the paper's practical conclusion is stated as 'potentially suited,' which is the right strength. Minor: Table I noise curves are pre-conceptual and the authors say so; the numerical integrals in Eqs. (33)–(34) I did not reproduce. Who should read it: anyone doing stochastic-background data analysis for space missions, and anyone who needs the complex-gamma filter. The formalism is the durable part; the numbers are a snapshot of 2005 mission concepts. Send it out. The filter derivation deserves referee attention and the forecast section will generate useful argument.

Referee report

Significance

The methodological contribution is real and useful: Eqs. (18)-(25) generalize the standard optimal-filter treatment to complex γ_IJ and to backgrounds whose amplitude is not negligible compared with the instrumental noise, and the paper verifies the latter point numerically in Fig. 4 rather than asserting it. The forecast itself is falsifiable and quantitative, and the paper is candid about the foreground problem: Sec. IV.B and Fig. 3 show explicitly that a 0.2 Hz cutoff moves the TDI-DECIGO/BBO reach by nearly three orders of magnitude and reverses the ranking between the two designs. The multipole-resolved sensitivity in Fig. 5, with its band-like structure favoring even ℓ, is a genuinely useful design input. The paper does not oversell: the abstract's '10⁻¹⁵ ~ 10⁻¹⁶' is the post-cutoff number, and the conditional on foreground subtraction is stated. The main open item is that the second foreground channel the authors themselves raise is left unquantified, so the design ranking in Sec. V rests on a single modeling choice.

Major objections (4)

[Sec. IV.B, Eq. (34), abstract sentence s4] The abstract's conditional ('as long as foreground point sources are properly subtracted') covers only resolvable point sources, but Sec. IV.B raises a second channel that is not point-like and is not quantified: 'there might exist a large confusion noise arising from cosmological supernovae and/or hypothetical early population of massive stars [34], which could dominate over the GWB of inflationary origin.' Because the integrand of Eq. (16) falls roughly as f⁻² at low frequency, the reach is controlled by the lowest frequencies in band, so a residual confusion floor above 0.2 Hz would degrade the FP-DECIGO number in Eq. (34) directly. Please attach at least an order-of-magnitude estimate, or a scaling of the reach with residual confusion amplitude, and broaden the abstract's conditional so that it covers confusion noise as well as point sources.
[Sec. IV.B, Eqs. (32) and (40)] The two effective-strain definitions are not mutually consistent, despite the text's claim that Eq. (40) 'correctly recovers' Eq. (32) at ℓ = 0. Inverting Eq. (16) for a band Δf gives h_eff = SNR^{1/2} {(5/2)² N_I N_J / (|γ_IJ|² Δf T_obs)}^{1/4}, whereas Eq. (32) as printed has (5/2) and |γ_IJ| to the first power inside the fourth root. Substituting σ_0² = 4π|(2/5)γ_IJ|² into Eq. (40) gives yet a third scaling, with |γ_IJ|^{1/2} in the numerator. Since Figs. 2 and 5 are plotted from these expressions, please identify the correct form and replot if necessary; the headline numbers in Eqs. (33)-(34) come from direct integration of Eq. (16) and are unaffected.
[Sec. IV.B, Fig. 3 and Eq. (34)] TDI-DECIGO/BBO and ultimate DECIGO share the same arm length (5×10⁷ m) and the same TDI X-variable readout, so their noise curves differ only by the overall shot- and acceleration-noise amplitudes in Eq. (B3). The quoted cutoff degradation factors nevertheless differ by more than an order of magnitude: 6.8×10⁻¹⁸ → 5.8×10⁻¹⁵ (factor ≈850) for TDI-DECIGO/BBO versus 4.2×10⁻²¹ → 1.2×10⁻¹⁹ (factor ≈29) for ultimate DECIGO. Please explain where this difference comes from — presumably the frequency at which shot noise overtakes acceleration noise in Eq. (B3) — since Fig. 3 is the figure on which the FP-DECIGO preference in Sec. V rests.
[Sec. IV.C, Eqs. (38)-(39)] It is not stated whether the dipole and quadrupole thresholds in Eqs. (38)-(39) are computed with the same f_cut = 0.2 Hz cutoff applied in Eq. (34), nor what spectral tilt N = d ln S_h / d ln f is assumed in Eq. (35). For a flat Ω_gw spectrum S_h ∝ f⁻³, so N = −3 and the dipole amplitude is 3β; the quoted thresholds scale linearly in Nβ and would shift accordingly. Please state both the integration band and the assumed tilt, so that the anisotropy numbers can be compared on the same footing as the isotropic reach.

Minor objections (10)

[Eq. (33)] The flat-spectrum ansatz is written 'Ω_gw(f) = Ω_gw,0 f⁰'; the trailing f⁰ is redundant and reads as a typo. Write Ω_gw(f) = Ω_gw,0.
[Eq. (2)] The angular delta function is written δ²(Ω, Ω'); it should presumably be δ²(Ω − Ω') to match the standard plane-wave normalization.
[Sec. III.A, after Eq. (22)] The sentence reads 'the SNR SNR as well as the optimal filter'; one of the duplicated 'SNR' tokens should be deleted.
[Sec. IV.B, text near Fig. 3] The text says the minimum detectable amplitude for f_cut ≳ 0.1 Hz 'becomes 100 times worse', while Eq. (34) implies a factor of about 850 at f_cut = 0.2 Hz. Please reconcile the wording with the numbers.
[Sec. IV.C and Sec. V] 'isotopic' appears where 'isotropic' is meant (e.g., 'the isotopic component of GWB', 'would not probe isotopic GWBs').
[Title, abstract, and throughout] The arXiv source has broken words that should be repaired in the typeset version: 'next-gene ration' in the title, 'op erated', 'stochasti c', 'T DI-DECIGO', 'ﬁler' for 'filter', and 'h²Ωgw' rendered as 'h²Ωgw' in the abstract.
[Fig. 1 caption] The caption says one of the three interferometers consists of six spacecrafts, while the text says two of the three consist of three spacecrafts each and the remaining one of six. Please make the caption consistent with the text.
[Table I] The caption describes the Ultimate DECIGO entries as an 'effective noise level', but the column headings are S_shot and S_accel. Please state explicitly whether these numbers enter Eq. (B3) in the same way as for TDI-DECIGO/BBO, or whether a different noise model was used.
[Appendix C, Fig. 6] The decay of C_IJ(f; t, t+δt) is demonstrated using the TDI A-variable, whereas the main analysis uses the X-variable. A sentence noting that the characteristic time T_* is the same for both would close the gap.
[Sec. II] 'Provided several independent output data, the correlation analysis is examined' is awkward; consider 'Given several independent output data streams, the correlation analysis proceeds'.

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The paper

The paper claims

The paper works out how faint a primordial gravitational-wave background the proposed post-LISA space interferometers could detect, and shows the answer depends as much on subtracting the astrophysical foreground as on the instrument.

The reading

The paper asks how faint a primordial gravitational-wave background the proposed follow-ons to LISA could actually detect in the 0.1 to 10 Hz band. Its answer is built on an upgraded version of the standard cross-correlation search: the authors generalize the optimal filter to the case where the overlap between two detectors is a complex function of frequency, which happens for Doppler-tracking space interferometers but not for ground-based ones. Feeding in the noise budgets of TDI-DECIGO/BBO, FP-DECIGO and an idealized ultimate DECIGO, they quote minimum detectable amplitudes $h^2Ω_{gw}$ of $6.8×10^{-18}$, $1.1×10^{-16}$ and $4.2×10^{-21}$ respectively, for one year of observation at signal-to-noise 5. They then show the ranking flips once the unresolved white-dwarf binary foreground is excised below 0.2 Hz: the TDI-DECIGO/BBO limit degrades to $5.8×10^{-15}$, while FP-DECIGO holds at $4.8×10^{-16}$, which is why the abstract quotes $10^{-15}$ to $10^{-16}$ rather than the more optimistic numbers. A final section asks whether the same correlation machinery could see the dipole anisotropy imprinted on the background by the Solar System's motion.

What carries the argument

The load-bearing device is a generalized optimal filter for the cross-correlation statistic $S_{IJ} = ∫∫ s_I(t')s_J(t'')Q(t'-t'')$, derived by replacing the usual inner product $(A|B)$ with a two-component inner product $｛A|B｝ = ∫_0^∞ (df/2) A^† M B$ built from the matrix $M = ((W, V^*),(V, W))$, where $V$ and $W$ collect the signal and noise variance terms. This is what allows the filter to be optimized when the overlap-reduction function $γ_{IJ}(f)$ is complex, as it is for Doppler-tracking space interferometers, whereas the earlier ground-based treatment assumed a real $γ$. The resulting filter and signal-to-noise reduce to $Q(f) = (2/5)S_h γ^*_{IJ}/R(f)$ and $SNR = √(2T_{obs}) [∫ (df/2)(2/5)^2 S_h^2 |γ_{IJ}|^2 / R]^{1/2}$, with $R$ containing the self-correlation terms $γ_{II}γ_{JJ}$ and the noise products $N_I N_J$; the paper also argues in a footnote that the variance stays positive definite for complex $C_{IJ}$ by a Schwarz-inequality step. For the anisotropic case the correlation signal is expanded in harmonics of the orbital period, $C_{IJ,m}(f)$, and the angular response is compressed into a rotationally invariant power $σ_ℓ^2(f)$ per multipole, from which an effective strain sensitivity $h^{(ℓ)}_{eff}(f)$ follows.

Extended reading notes

Core claim

The central claim is a sensitivity forecast rather than a detection: with a generalized optimal filter and realistic instrumental noise, a cross-correlation search with next-generation space interferometers can reach $h^2Ω_{gw} ≈ 10^{-15}$ to $10^{-16}$ around 0.1 to 10 Hz, provided foreground point sources are subtracted. The forecast is explicitly conditional. Without any foreground cut the reach is far better ($6.8×10^{-18}$ for TDI-DECIGO/BBO), but the paper argues that cosmological white-dwarf binaries form a confusion noise below roughly 0.2 Hz that must be discarded, and that this single choice moves the TDI-DECIGO/BBO limit by about two orders of magnitude while barely touching FP-DECIGO, whose better sensitivity sits at higher frequency. The secondary claim is that the same formalism extends to anisotropies: the dipole induced by the observer's proper motion, with the CMB dipole direction and $β = 1.23×10^{-3}$ as the template, would need an isotropic component of roughly $h^2Ω_{gw} ≳ 10^{-11}$ to be detectable, because the antenna response of the proposed spacecraft constellations is strong only for low even multipoles.

Load-bearing premise

The headline numbers assume the unresolved astrophysical foreground can be treated as a sharp wall at 0.2 Hz below which all data are thrown away, and that everything above it can be cleaned out; if that wall sits higher, or leaks above 0.2 Hz, the quoted reach and the ranking between the two designs both change by orders of magnitude.

Editorial extensions

If this is right

A cross-correlation search with a star-like six-spacecraft constellation reaches roughly seven orders of magnitude below the LISA single-detector limit, so the 0.1 to 1 Hz band becomes a genuine target for an inflationary background.
Because the low-frequency foreground cut costs TDI-DECIGO/BBO two orders of magnitude but leaves FP-DECIGO nearly unchanged, a Fabry-Perot design at shorter arm length is the configuration that survives realistic foregrounds.
The weak-signal approximation used throughout is self-consistent only while $Ω_{gw} ≲ 10^{-15}$; above that the signal itself enters the variance and the simple filter overestimates the signal-to-noise by an increasing margin.
Detecting the velocity dipole of the background requires an isotropic amplitude of order $10^{-11}$, which the known binary foreground may supply even when the primordial component does not.
The angular response of these constellations is concentrated in multipoles $ℓ = 0, 2, 4$ with weak odd-$ℓ$ response, so any attempt at background anisotropy mapping is limited to a handful of low multipoles.

Reading between the lines

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

If the foreground subtraction were done by actually fitting and removing resolved binaries rather than by a hard cutoff, the effective sensitivity would depend on how many sources a precursor mission resolves, which is a different and probably more favourable calculation than the one presented here.
The same complex-$γ$ generalization should apply to any space mission whose signal extraction uses time-delayed combinations, so the filter derived here is likely reusable for configurations beyond the three named designs.
The dipole forecast effectively turns the search into a cross-check on the CMB rest frame; a measured mismatch between the two dipole directions would itself be evidence that the low-frequency background is astrophysical rather than primordial.
The paper's own caveat that supernovae or an early massive-star population could add confusion noise above 0.2 Hz suggests the cutoff should be treated as a lower bound on the difficulty, not a fixed parameter.

Original abstract

Future missions of gravitational-wave astronomy will be operated by space-based interferometers, covering very wide range of frequency. Search for stochastic gravitational-wave backgrounds (GWBs) is one of the main targets for such missions, and we here discuss the prospects for direct measurement of isotropic and anisotropic components of (primordial) GWBs around the frequency 0.1-10 Hz. After extending the theoretical basis for correlation analysis, we evaluate the sensitivity and the signal-to-noise ratio for the proposed future space interferometer missions, like Big-Bang Observer (BBO), Deci-Hertz Interferometer Gravitational-wave Observer (DECIGO) and recently proposed Fabry-Perot type DECIGO. The astrophysical foregrounds which are expected at low frequency may be a big obstacle and significantly reduce the signal-to-noise ratio of GWBs. As a result, minimum detectable amplitude may reach h^2 \ogw = 10^{-15} \sim 10^{-16}, as long as foreground point sources are properly subtracted. Based on correlation analysis, we also discuss measurement of anisotropies of GWBs. As an example, the sensitivity level required for detecting the dipole moment of GWB induced by the proper motion of our local system is closely examined.

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, 5,783 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.79 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.97 · compares with prior results 0.14 · 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.

Future missions of gravitational-wave astronomy will be operated by space-based interferometers, covering very wide range of frequency. Search for stochastic gravitational-wave backgrounds (GWBs) is one of the main targets for such missions, and we here discuss the prospects for direct measurement of isotropic and anisotropic components of (primordial) GWBs around the frequency 0.1-10 Hz. After extending the theoretical basis for correlation analysis, we evaluate the sensitivity and the signal-to-noise ratio for the proposed future space interferometer missions, like Big-Bang Observer (BBO), Deci-Hertz Interferometer Gravitational-wave Observer (DECIGO) and recently proposed Fabry-Perot type DECIGO. The astrophysical foregrounds which are expected at low frequency may be a big obstacle and significantly reduce the signal-to-noise ratio of GWBs. As a result, minimum detectable amplitude may reach h^2 \ogw = 10^{-15} \sim 10^{-16}, as long as foreground point sources are properly subtracted. Based on correlation analysis, we also discuss measurement of anisotropies of GWBs. As an example, the sensitivity level required for detecting the dipole moment of GWB induced by the proper motion of our local system is closely examined.

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	Future missions of gravitational-wave astronomy will be operated by space-based interferometers, covering very wide range of frequency.	background 1.00	0.04	0.02	asserted 0.96
s1	Search for stochastic gravitational-wave backgrounds (GWBs) is one of the main targets for such missions, and we here discuss the prospects for direct measurement of isotropic and anisotropic components of (primordial) GWBs around the frequency 0.1-10 Hz.	background 0.63	0.18	0.07	asserted 1.00
s2	After extending the theoretical basis for correlation analysis, we evaluate the sensitivity and the signal-to-noise ratio for the proposed future space interferometer missions, like Big-Bang Observer (BBO), Deci-Hertz Interferometer Gravitational-wave Observer (DECIGO) and recently proposed Fabry-Perot type DECIGO.	contribution 0.69	0.83	0.06	asserted 0.97
s3	The astrophysical foregrounds which are expected at low frequency may be a big obstacle and significantly reduce the signal-to-noise ratio of GWBs.	background 0.52	0.11	0.05	hedged possibility 0.99
s4	As a result, minimum detectable amplitude may reach h^2 \ogw = 10^{-15} \sim 10^{-16}, as long as foreground point sources are properly subtracted.	result 1.00	0.68	0.52	hedged possibility 0.99
s5	Based on correlation analysis, we also discuss measurement of anisotropies of GWBs.	contribution 0.94	0.72	0.05	asserted 0.69
s6	As an example, the sensitivity level required for detecting the dipole moment of GWB induced by the proper motion of our local system is closely examined.	contribution 0.86	0.73	0.06	asserted 0.81

What kind of paper the classifier reports this is: theoretical result 0.77 · 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

Figures

**Figure 1.** FIG. 1: A typical orbital configuration for a future space int

**Figure 2.** FIG. 2: Spectral amplitude sensitivity

**Figure 3.** FIG. 3: Dependence of low-frequency cutoff

**Figure 5.** FIG. 5: Effective strain amplitude

Showing 5 of the paper's 6 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:gr-qc/0511145 by the authors.

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High-frequency gravitational waves from axion inflation in the weak-backreaction regime
hep-ph 2026-07 conditional novelty 6.0 of 10

Even in the weak-backreaction regime, axion inflation produces high-frequency primordial gravitational waves many orders of magnitude above the vacuum spectrum, peaking around MHz–GHz.

Show 55 more citing papers

Leptogenesis with sub-electroweak-scale reheating temperature
hep-ph 2026-07 conditional novelty 6.0 of 10

Leptogenesis remains viable for reheating temperatures below sphaleron freeze-out in three perturbative monomial-inflaton scenarios, with blue-tilted primordial GWs as a potential probe.
Primordial Black Hole from Tensor-induced Density Fluctuation: First-order Phase Transitions and Domain Walls
astro-ph.CO 2026-05 unverdicted novelty 6.0 of 10

Tensor perturbations from FOPT and domain-wall sources are claimed to induce second-order scalar perturbations large enough to form primordial black holes, potentially all of the dark matter.
Smoluchowski Coagulation Equation and the Evolution of Primordial Black Hole Clusters
astro-ph.CO 2026-04 unverdicted novelty 6.0 of 10

Monte Carlo solutions to the Smoluchowski coagulation equation yield runaway timescales and mass evolution for primordial black hole clusters at different redshifts based on cluster properties.
Anisotropic Gravitational Waves from Anisotropic Axion Rotation
hep-ph 2025-08 conditional novelty 6.0 of 10

A transiently dominant rotating axion sources an induced gravitational wave background whose amplitude and large-scale anisotropy trace the axion's isocurvature fluctuations, with detection prospects for BBO and DECIGO.
Unveiling the inert Triplet desert region with a pNGB Dark Matter and its Gravitational Wave signatures
hep-ph 2025-05 conditional novelty 6.0 of 10

A two-component dark matter model combining an inert scalar triplet with a pseudo-Goldstone singlet revives the sub-TeV triplet desert region and predicts gravitational waves detectable by LISA, BBO, and DECIGO.
Prospecting bipartite Dark Matter through Gravitational Waves
hep-ph 2024-12 conditional novelty 6.0 of 10

A two-component dark matter model with an inert triplet scalar and a singlet fermion can explain the relic abundance while producing a strong electroweak phase transition and gravitational wave signals detectable by L...
Gravitational Wave from Graviton Bremsstrahlung during Reheating
hep-ph 2023-01 conditional novelty 6.0 of 10

Two independent recomputations of the inflaton's three-body decay into matter plus a graviton agree with each other and disagree with three earlier published results, yielding a GHz-to-THz gravitational wave backgroun...
Kination cosmology from scalar fields and gravitational-wave signatures
hep-ph 2021-11 conditional novelty 6.0 of 10

An intermediate kination era inside the radiation epoch, naturally produced by spinning axion fields, imprints a peaked gravitational-wave spectrum whose position and height map onto axion dark-matter parameters.
Measuring the net circular polarization of the stochastic gravitational wave background with interferometers
astro-ph.CO 2019-10 conditional novelty 6.0 of 10

A kinematic dipole lets planar detectors such as LISA and ET measure the net circular polarization of the stochastic gravitational wave background at signal-to-noise of order one for h^2 Omega_GW about 10^-11.
Encyclopaedia Inflationaris
astro-ph.CO 2013-03 accept novelty 6.0 of 10

The authors release ASPIC and an encyclopaedic set of slow-roll, reheating-consistent predictions for 118 single-field inflation models.
Axion cosmology with long-lived domain walls
hep-ph 2012-07 conditional novelty 6.0 of 10

Lattice simulations show long-lived axion domain walls radiate mildly relativistic axions, overproducing cold dark matter and excluding post-inflationary models with domain wall number greater than one unless the bias...
Prospects for direct detection of primordial gravitational waves
astro-ph 2006-02 conditional novelty 6.0 of 10

Single-field inflation models consistent with the 2006 CMB constraints produce a primordial gravitational wave background at 1 mHz to 1 Hz no larger than about 1.6 times 10 to the minus 15.
Scale-Invariant Three-Component Dark Matter and Gravitational Wave Signals
hep-ph 2026-11 accept novelty 5.0 of 10

A three-component dark matter model with classical scale invariance predicts a first-order electroweak phase transition and a gravitational wave signal within reach of BBO and DECIGO.
Impact of Bubble Nucleation History and Friction on Primordial Black Hole Formation
hep-ph 2026-08 conditional novelty 5.0 of 10

Bubble-wall friction and the nucleation-rate shape strongly alter primordial black hole mass and formation time in delayed first-order phase transitions, while gravitational-wave spectra alone cannot distinguish the t...
Gravitational Wave Imprints of a High-Quality Axion and the Origin of Flavor Hierarchies
hep-ph 2026-06 unverdicted novelty 5.0 of 10

Gauged U(1)_F flavor symmetries shield the axion from quantum gravity corrections, yielding unit domain wall number and a plateau-valley GW spectrum from flavonic and axionic strings as a probe of flavored axion dark matter.
Probing Bose-enhanced Inflaton Decay with Gravitational Waves
hep-ph 2026-01 unverdicted novelty 5.0 of 10

Bose enhancement from a transient condensate of inflaton decay products dramatically increases decay efficiency and amplifies stochastic gravitational wave production to potentially observable levels.
Stochastic Gravitational Waves from Modulated Reheating
astro-ph.CO 2025-10 unverdicted novelty 5.0 of 10

A spectator scalar in modulated reheating with large Higgs-like couplings generates detectable scalar-induced stochastic gravitational waves for BBO and DECIGO, but only outside perturbative low-energy extrapolations.
Cogenesis of baryon and lepton number asymmetries matching the EMPRESS Data
hep-ph 2025-09 conditional novelty 5.0 of 10

A U(1)_{B-L} flaton decay chain can produce both a large positive electron-neutrino asymmetry and the observed baryon asymmetry, with values matching EMPRESS and BBN for a symmetry-breaking scale around 10^10 GeV.
Gravitational Wave Signature and the Nature of Neutrino Masses: Majorana, Dirac, or Pseudo-Dirac?
hep-ph 2025-09 unverdicted novelty 5.0 of 10

In the minimal B-L gauge extension, Majorana neutrinos at high breaking scale produce flat GW spectra from cosmic strings, Dirac at low scale produce peaked spectra from first-order phase transitions, and pseudo-Dirac...
Little Red Dots from Small-Scale Primordial Black Hole Clustering
astro-ph.CO 2025-07 conditional novelty 5.0 of 10

Densely clustered 30-solar-mass primordial black holes can sequentially merge into ~10^6 solar-mass seeds by redshift 6, possibly explaining JWST little red dots, with high spin from tidal torques and a two-peak gravi...
Dark clouds to silver linings over the hyperchargeless scalar triplets
hep-ph 2025-05 conditional novelty 5.0 of 10

Under current constraints, the inert triplet model is insufficient for dark matter and for a first-order phase transition, while the non-inert triplet model retains a narrow 150 to 275 GeV window for a strong two-step...
One-loop corrections to the E-type $\alpha$-attractor models of inflation and primordial black hole production
gr-qc 2025-02 conditional novelty 5.0 of 10

For E-type alpha-attractor inflation models tuned to produce asteroid-mass primordial black holes, the one-loop correction from cubic interactions is only a few percent of the tree-level power spectrum.
NANOGrav signal from axion inflation
hep-ph 2023-07 conditional novelty 5.0 of 10

Axion inflation with a massive gauge field can generate a parity-violating gravitational wave background at nano-Hz frequencies, and a two-parameter fit to NANOGrav 15-year data leaves a viable parameter region.
Correlating Gravitational Waves with $W$-boson Mass, FIMP Dark Matter, and Majorana Seesaw Mechanism
hep-ph 2022-04 conditional novelty 5.0 of 10

In a scotogenic model with right-handed neutrinos, the mass splitting that fits the CDF W-boson mass also strengthens the electroweak phase transition and yields a gravitational-wave signal near U-DECIGO sensitivity.
Supercool Composite Dark Matter Beyond 100 TeV
hep-ph 2021-10 conditional novelty 5.0 of 10

Supercooled confinement in a nearly-conformal dark sector, with dilaton-mediated interactions, can yield the observed dark matter abundance for masses up to 10^6 TeV, a range testable entirely by future gravitational ...
Measuring the spectrum of primordial gravitational waves with CMB, PTA and Laser Interferometers
astro-ph.CO 2020-07 conditional novelty 5.0 of 10

A unified forecast shows that combining CMB and space-based interferometer data could map the primordial gravitational-wave spectrum across many frequency decades, provided astrophysical foregrounds can be cleaned as assumed.
Primordial black holes from modified supergravity
hep-th 2020-06 conditional novelty 5.0 of 10

Modified supergravity with a second scalar produces a two-stage inflation whose ultra-slow-roll phase generates primordial black holes that can account for the dark matter, for tuned couplings and masses near 10^18 to...
Thermally modified sterile neutrino portal dark matter and gravitational waves from phase transition: The Freeze-in case
hep-ph 2018-10 conditional novelty 5.0 of 10

Finite-temperature masses and shifting vacuum expectation values during a two-step electroweak phase transition open and close freeze-in dark matter production channels, leaving step-like features in the relic abundan...
Fingerprinting models of first-order phase transitions by the synergy between collider and gravitational-wave experiments
hep-ph 2018-09 conditional novelty 5.0 of 10

Fisher-matrix forecasts indicate that LISA, DECIGO and BBO could measure phase-transition parameters, and through them the couplings of three new-physics models, in ways that complement future collider measurements.
Resonant Di-Higgs Production at Gravitational Wave Benchmarks: A Collider Study using Machine Learning
hep-ph 2018-08 conditional novelty 5.0 of 10

For two xSM benchmark points, a boosted-decision-tree analysis of the b-bbar + photon-photon channel claims 6.1 sigma (BM5) and 3.2 sigma (BM7) sensitivity at 3 ab^-1, alongside LISA signal-to-noise ratios above 10.
Explore Inert Dark Matter Blind Spots with Gravitational Wave Signatures
hep-ph 2017-04 conditional novelty 5.0 of 10

Gravitational waves from a strong first-order phase transition can probe the blind spot of inert scalar dark matter models, where the Higgs-DM coupling vanishes and direct detection fails.
Gravitational Wave Signals of Electroweak Phase Transition Triggered by Dark Matter
hep-ph 2017-02 conditional novelty 5.0 of 10

A Standard Model extended by two scalar singlets can produce a strongly first order two-step electroweak phase transition with a viable dark matter relic density, and the gravitational waves for one benchmark point fa...
Gravitational waves from the asymmetric-dark-matter generating phase transition
hep-ph 2017-02 conditional novelty 5.0 of 10

For the Petraki-Trodden-Volkas asymmetric dark matter model, the phase transition is strong enough that a subset of parameter space gives gravitational waves detectable by BBO, but only a small corner reaches LISA sen...
Observable induced gravitational waves from an early matter phase
astro-ph.CO 2013-03 conditional novelty 5.0 of 10

An early matter-dominated phase lowers the reheat temperature and boosts second-order induced gravitational waves into the sensitivity band of DECIGO, BBO and Advanced LIGO for hilltop and running-mass inflation models.
Observable Spectra of Induced Gravitational Waves from Inflation
astro-ph.CO 2012-03 conditional novelty 5.0 of 10

Hilltop-type inflation with integral coupling powers produces induced gravitational waves detectable by BBO/DECIGO after a reasonable number of e-folds, whereas the running mass model requires an unreasonably short inflation.
Prospects for determination of thermal history after inflation with future gravitational wave detectors
astro-ph.CO 2011-10 conditional novelty 5.0 of 10

Fisher-matrix forecasts indicate that DECIGO/BBO-class detectors could pin the reheating temperature near 10^7 GeV and distinguish matter, radiation, and kination eras if the tensor-to-scalar ratio is around 0.1.
Gravitational-Wave Constraints on the Abundance of Primordial Black Holes
astro-ph.CO 2009-12 conditional novelty 5.0 of 10

Induced gravitational waves from the density peak that forms primordial black holes are large enough for planned space-based and atomic interferometers to detect black holes of 10^20 to 10^26 grams, even when the peak...
Probing polarization states of primordial gravitational waves with CMB anisotropies
astro-ph 2007-05 conditional novelty 5.0 of 10

A circularly polarized inflationary gravitational wave background produces TB and EB CMB spectra that reionization boosts at large angles, and a cosmic-variance-limited experiment could detect a polarization degree ab...
The cosmological gravitational wave background from primordial density perturbations
gr-qc 2006-12 conditional novelty 5.0 of 10

Second-order primordial density perturbations during the radiation era produce a gravitational wave background whose spectrum could let future detectors constrain the primordial power spectrum at scales some twenty or...
Gravitational waves in the complex-singlet-extended Manohar-Wise model
hep-ph 2026-09 conditional novelty 4.0 of 10

In the complex-singlet-extended Manohar-Wise model, scanned benchmarks give first-order phase-transition gravitational-wave peaks near 10^-3 to 10^-2 Hz and a bias-tuned domain-wall peak near 2x10^-9 Hz that reaches p...
Scalar Portal Verifiable Light Dark Matter and Correlated Gravitational Wave Signatures
hep-ph 2026-09 conditional novelty 4.0 of 10

A scalar-portal p-wave dark matter model in a stiff pre-BBN cosmology simultaneously matches the relic density and predicts a correlated, potentially detectable high-frequency gravitational wave spectrum.
Gravitational Waves from hybrid defects as probe of Flavor symmetry breaking: Machine-Learning Approach
astro-ph.CO 2026-05 unverdicted novelty 4.0 of 10

Hybrid string-bounded domain wall networks from sequential U(1)_F and Z2 symmetry breaking generate a GW spectrum with a unique low-frequency slope that future detectors can observe and an MLP surrogate can characteri...
From WIMP to FIMP during reheating: collider vs non-collider probes for p-wave annihilation
hep-ph 2026-05 unverdicted novelty 4.0 of 10

Collider experiments can strongly constrain p-wave-suppressed derivative operators and thereby limit reheating temperature, DM mass, and interaction scale needed to match observed DM abundance during reheating.
Gamma-Rays and Gravitational Waves from Inelastic Higgs Portal Dark Matter
hep-ph 2025-07 conditional novelty 4.0 of 10

An inelastic complex-scalar Higgs portal dark matter model can evade direct detection, explain the Galactic Center gamma-ray excess, and produce a first-order electroweak phase transition with a gravitational wave sig...
Gravitational waves and dark matter with Witten effect
hep-ph 2025-01 conditional novelty 4.0 of 10

A dark SU(2) phase transition can produce monopole dark matter, make the axion heavy via the Witten effect, and generate nanohertz gravitational waves matching PTA hints.
Phase transition dynamics and gravitational wave spectra of strong first-order phase transition in supercooled universe
hep-ph 2020-03 conditional novelty 4.0 of 10

Evaluating strongly supercooled phase transitions at the percolation temperature rather than the nucleation temperature changes predicted gravitational wave amplitudes by large factors, and a new Tn < Tmin test flags ...
Gravitational waves from scale-invariant vector dark matter model: Probing below the neutrino-floor
hep-ph 2019-07 conditional novelty 4.0 of 10

For one benchmark point of a scale-invariant vector dark matter model whose direct-detection signal lies below the neutrino floor, the electroweak phase transition gravitational-wave spectrum is predicted to fall insi...
Gravitational waves induced by scalar perturbations as probes of the small-scale primordial spectrum
astro-ph.CO 2018-12 conditional novelty 4.0 of 10

Using an updated second-order gravitational-wave formula and proper signal-to-noise integration against detector sensitivity curves, the authors derive current and projected limits on the amplitude of small-scale prim...
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 ...
A new insight into the phase transition in the early Universe with two Higgs doublets
hep-ph 2017-12 conditional novelty 4.0 of 10

A strong first-order electroweak phase transition is achievable in the Type I and Type II two-Higgs-doublet models, and the critical-temperature field value correlates with the zero-temperature one-loop potential depth.
Gravitational wave and collider implications of electroweak baryogenesis aided by non-standard cosmology
hep-ph 2016-09 conditional novelty 4.0 of 10

A modified early-universe expansion history relaxes the sphaleron bound and extends the scalar mass range compatible with electroweak baryogenesis, and future Higgs precision measurements probe that range far better t...
Hearing the echoes of electroweak baryogenesis with gravitational wave detectors
hep-ph 2016-01 conditional novelty 4.0 of 10

A Higgs model with a sextic operator gives a strong first-order electroweak phase transition whose gravitational-wave spectrum peaks between 10^-4 and 1 Hz, detectable by eLISA, DECIGO and BBO, and correlates with a H...
Primordial blackholes and gravitational waves for an inflection-point model of inflation
astro-ph.CO 2013-07 conditional novelty 4.0 of 10

For inflection-point inflation, the present-day primordial black hole density is tied to the primordial gravitational wave density, and Planck data are used to quote a range near 0.00997 for the black hole density parameter.
The Search For Primordial Tensor Modes
astro-ph 2006-03 conditional novelty 4.0 of 10

A review of inflationary gravitational-wave searches concludes that experiments probing tensor-scalar ratios near 1e-2 are well motivated, while pushing to 1e-4 is poorly justified because inflation theory does not fi...
Indirect dark matter searches with neutrino telescopes via energetic cosmic showers
hep-ph 2025-09 reject novelty 3.0 of 10

Bounds on Z'-mediated dark matter are derived from neutrino telescopes, freeze-in, and cosmic strings, but the telescope bounds rest on comparing a Galactic-center flux to faraway sources.

See all 61 Pith citations

How later papers used it

144 later papers cite it

Evidence: substantial. 143 of the citing papers share no author with it, and 22 of those carry a confident label from Pith's citation classifier.

Pith read 13 of the 192 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

4 later papers by other authors are listed below: 2 used its method or tool and 2 used its data or values.

Uses its method or tool 2 of 8 papers with this label

Used this paper's optimal filter function that returns the signal-to-noise ratio.

Probing Leptogenesis at LISA: A Fisher analysis (2025) · 0.97 · paraphrased: the licence does not allow quoting
We quantify the SNR using the most general (for arbitrary signal strength) optimal filter function [ref] Q̃(f)=U(f)V(f)^*-U(f)^*W(f)/|V(f)|^2-W(f)^2 that returns SNR as [ref] SNR=√(2T_obs)[∫_-∞^+∞df/2|U(f)|^2/|U(f)|^2+W(f)]^1/2, where the frequency-dependent functions are given by U(f) = C_IJ(f) + δ_IJ N_I(f), V(f) = C_IJ^2 + δ_IJ N_I (N_I + 2C_II), W(f) = C_IIC_JJ + C_IIN_J + C_JJN_I + N_I N_J with C_IJ(f; t, t) = ∫dΩ/4π S_h(f) F_IJ(f, Ω; t, t), ⟨ñ^*_I(f) ñ_J(f')| ⟩= 1/2 δ_IJ δ(f - f') N_I(f) ⟨h̃^*_A(f, Ω) h̃_A'(f', Ω') ⟩ = 1/2 δ(f - f') δ^2(Ω, Ω') δ_AA'/4π S_h(|f|, Ω).

Cosmic superstrings, metastable strings and ultralight primordial black holes: from NANOGrav to LIGO and beyond (2024) · Numerical results: Expected Signal-to-Noise-Ratio at the Einstein Telescope · 1.00

Uses its data or values 2 of 7 papers with this label

Used this paper's results for FP-DECIGO.

Prospects for Direct Detection of Inflationary Gravitational Waves by Next Generation Interferometric Detectors (2010) · 0.89 · paraphrased: the licence does not allow quoting
Took the parameters of its Ultimate-DECIGO from this paper.

Prospects for determination of thermal history after inflation with future gravitational wave detectors (2011) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

135 arXiv papers cite this in 184 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 · 133 sentences without a confident label

Contests it 1 paper

where $S_shot=2.3×10^-24√((1+f^2/f_c^2)) Hz^-1/2$ is the shot noise [Here we have fixed a typo in Ref. [ref] as already done in [ref] .], $S_accel=2.0×10^-26/(f/Hz)^2 Hz^-1/2$ is the acceleration noise, and $S_rad=6.0 ×10^-26/[(f/Hz)^2 √(1+f^2/f_c^2)] Hz^-1/2$ is the radiation pressure noise, with $f_c=7.36$Hz being the cutoff frequency.

Implications of the B-mode Polarization Measurement for Direct Detection of Inflationary Gravitational Waves · Detectability of inflationary gravitational waves · contest 0.72

Uses its method or tool 8 papers

Q̃(f)=U(f)V(f)^*-U(f)^*W(f)/|V(f)|^2-W(f)^2 that returns SNR as [ref] SNR=√(2T_obs)[∫_-∞^+∞df/2|U(f)|^2/|U(f)|^2+W(f)]^1/2, where the frequency-dependent functions are given by U(f) = C_IJ(f) + δ_IJ N_I(f), V(f) = C_IJ^2 + δ_IJ N_I (N_I + 2C_II), W(f) = C_IIC_JJ + C_IIN_J + C_JJN_I + N_I N_J with C_IJ(f; t, t) = ∫dd̂/4π S_h(f) R_IJ(f, d̂; t, t), ⟨ñ^*_I(f) ñ_J(f')| ⟩= 1/2 δ_IJ δ(f - f') N_I(f) ⟨h̃^*_A(f, d̂) h̃_A'(f', d̂') ⟩ = 1/2 δ(f - f') δ^2(d̂, d̂') δ_AA'/4π S_h(|f|, d̂).

Probing Leptogenesis at LISA: A Fisher analysis · LISA instrumental noise, foregrounds, and Fisher matrix forecast · 0.97
The signal-to-noise ratio is given by [ref] [equation] where $t_obs$ is the observation time and $Ω_sens$ the sensitivity of the interferometer.

Primordial black holes as dark matter: Interferometric tests of phase transition origin · Signal-to-noise ratio · 0.97
The SNR is [ref] SNR^2 = 2 T ∫_-∞^∞ df/2 |U(f) |^2/|U(f) |^2 + W(f) , where U(f) = C_12(f) , W(f) = C_11(f) C_22(f)+C_11(f)N_2(f)+C_22(f)N_1(f)+N_1(f)N_2(f) .

Precision Early Universe Cosmology from Stochastic Gravitational Waves · SNR and Fisher matrix · 0.84

Uses its data or values 7 papers

We also include several other proposed experiments, i.e. Taiji GW project, Big Bang Observer (BBO), DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) [ref] , and Ultimate-DECIGO (UDECIGO) [ref] .

Using LISA-like Gravitational Wave Detectors to Search for Primordial Black Holes · Introduction · 0.81
The forecasts established in these studies indicate that while BBO will be competitive with Planck ($Δn_T ∼0.1$), upgrades to BBO might achieve $Δn_T ∼10^-2$, and DECIGO might reach $Δn_T ∼10^-3$ [ref] in the most optimistic cases.

Optimizing future experimental probes of inflation · Tensor Index · 0.89
We assume that future experiments determine the value of $Ω_GW$ with an accuracy of [ref] [equation] which is derived from the sensitivity of the BBO experiment (Detailed values for computing the noise spectrum are given in Ref. [ref] ).

Higher Order Corrections to the Primordial Gravitational Wave Spectrum and its Impact on Parameter Estimates for Inflation · $ϕ^2$ model · 0.88

Compares with it 6 papers

As shown in Fig. [ref], the predicted spectra are mostly outside the reach of near-future detectors such as LISA [ref] , DECIGO [ref] , and BBO [ref] , but they fall within the sensitivity ranges of more advanced detectors such as Ultimate-DECIGO [ref] and the recently proposed $μ$-ARES [ref] .

Complementarity between gravitational wave signatures and Higgs precision measurements of a classically conformal hidden U(1) extended Standard Model · GWs from the Classically Conformal $U(1)_H$ extended SM · 0.83
The produced results has been compared with the predictions from various GW interferometers LISA, BBO, DECIGO and others [ref] .

The N2HDM, Entropy Production and Stochastic Gravitational Waves · Stochastic Gravitational Waves · 0.91
The results are shown together with the projected sensitivities expected in LISA, and the planned u-DECIGO and BBO missions [ref] .

Gravitational footprints of massive neutrinos and lepton number breaking · Inverse seesaw with majoron: small $v_σ$ case · 0.84

Cites it as background 25 papers

Such a GW signal can be detected in LISA [ref] , or other proposed ground-based and space-borne experiments, viz., ALIA [ref] , Taiji [ref] , TianQin [ref] , aLigo+ [ref] , Big Bang Observer (BBO) [ref] and Ultimate(U)-DECIGO [ref] , if the amplitude is high enough.

Interplay among gravitational waves, dark matter and collider signals in the singlet scalar extended type-II seesaw model · Introduction · 0.82
Additionally, during the phase transition (PT) [ref] [See Ref. [ref] for a brief review.], plausible emission of gravitational waves (GWs) [ref] [The appearance of the GWs depends on bubble collision [ref] , turbulence in primordial plasma [ref] , and sonic waves [ref] .], could be detected by space-based GW interferometers, such as, SKA [ref] , $μ$-Ares [ref] , LISA [ref] , BBO [ref] , DECIGO, U-DECIGO, and U-DECIGO-corr [ref] , AEDGE [ref] , AION [ref] , CE [ref] , ET [ref] , future upgrades of LVK [ref] , etc.

Prospecting bipartite Dark Matter through Gravitational Waves · Introduction · 0.96
The next band is mHz to Hz which will be investigated by planned laser interferometers LISA [ref] , BBO [ref] and DECIGO [ref] and atomic interferometers AION [ref] and AEDGE [ref] .

Gravitational Wave Probes of Massive Gauge Bosons at the Cosmological Collider · Gravitational Wave Signatures · 0.91

Discussion

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