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Revisiting holographic dark energy from the perspective of multi-messenger gravitational wave astronomy: future joint observations with short gamma-ray bursts

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Gravitational-wave standard sirens from third-generation detectors, combined with a THESEUS-like short gamma-ray burst detector, would sharpen holographic dark energy constraints substantially, improving H0, c, and Omega_m by 63-88%…

desk verdict A competent and mostly honest forecast of HDE/RDE constraints from 3G GW–GRB standard sirens; the claimed improvements are real but rest on unexamined astrophysical rate assumptions. read the letter →

arxiv 2412.06873 v2 pith:IYYFQLDK submitted 2024-12-09 astro-ph.CO astro-ph.HEgr-qchep-ph

Tao Han , Ze Li , Jing-Fei Zhang , Xin Zhang This is my paper · ORCID
classification astro-ph.COastro-ph.HEgr-qchep-ph MSC 83F05 PACS 98.80.-k95.36.+x04.30.-w
keywords gravitationalwavesstandardsirensholographicdarkenergyshortgamma-rayburstsHubbleconstantthird-generationdetectorscosmologicalparameterestimationFishermatrixforecast
topics Dark Energy
open problems Dark Energy
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 argues that in the coming era of third-generation gravitational-wave detectors, joint observations with a short gamma-ray burst satellite like THESEUS can turn binary neutron star mergers into cosmological distance rulers, and that this would matter specifically for testing holographic dark energy. It simulates ten years of such events and finds that gravitational-wave data alone measure the Hubble constant H0 to 0.2-0.6%, but leave other cosmological parameters poorly constrained. When added to a mainstream combination of CMB, baryon acoustic oscillations, and supernova data, the simulated standard sirens break parameter degeneracies and improve the constraints on H0, the holographic parameter c, and the matter density Omega_m by 63-88%, 27-44%, and 55-70% respectively. If this forecast is correct, it offers an independent, near-sub-percent measurement of H0 that bears directly on the Hubble tension and a much sharper test of whether dark energy behaves as phantom energy in the holographic picture.

What carries the argument

The central mechanism is the simulated GW-GRB standard-siren catalog. Binary neutron star mergers are generated from the Madau-Dickinson star formation rate with a power-law delay distribution P(td) proportional to 1/td, a local merger rate of 920 $Gpc^{-3}$ $yr^{-1}$, and a Gaussian jet profile with core angle theta_c = 4.7 degrees. Detectability is set by a gravitational-wave signal-to-noise threshold of 12, a short-GRB flux threshold corresponding to THESEUS, and a broken-power-law luminosity function with parameters alpha_L = -1.95, beta_L = -3, and L* = 2 x $10^{52}$ erg/s. Luminosity-distance errors come from a Fisher information matrix, with weak-lensing and peculiar-velocity contributions added. The paper includes Earth's rotation in the detector response, considers single ET, single CE, CE-CE, and ET-CE-CE networks, and treats both optimistic and realistic gamma-ray burst field-of-view scenarios. The degeneracy-breaking effect arises because GW standard sirens measure dL(z) with a very different angular-degeneracy structure than CMB, BAO, and supernova data.

What would settle it

Compare the predicted standard-siren yield, 363 events for ET2CE in the optimistic scenario and 121 in the realistic scenario over ten years, plus their redshift distribution, against actual 3G-era observations. If a real ET2CE-plus-THESEUS campaign detects far fewer coincident GW-GRB events, or the luminosity-distance errors are significantly larger than the Fisher-matrix prediction, the forecasted improvements shrink accordingly. A cheaper check is to rerun the same Fisher forecast with the local merger rate at the lower end of the GWTC-3 range and see whether the improvement percentages drop substantially.

Watch

Extended reading notes

Core claim

The central claim is that a multi-messenger campaign pairing 3G gravitational-wave detectors with a THESEUS-like gamma-ray burst detector will produce enough standard sirens to transform holographic dark energy constraints. For the HDE model, the ET2CE network, the best configuration studied, yields 363 standard sirens in the optimistic scenario and 121 in the realistic scenario over ten years. Adding this simulated dataset to the CMB+BAO+SN (CBS) combination improves the error on H0 by 63.2-88.4%, on the holographic parameter c by 26.8-43.9%, and on Omega_m by 55.2-70.1%, depending on the detector network and gamma-ray burst field-of-view scenario. The authors attribute this gain to the different degeneracy orientation of standard-siren distance measurements compared with electromagnetic cosmological probes. They also find that GW data alone achieve H0 precision of 0.18-0.64% in the HDE model, while remaining weak for c and Omega_m, and they report similar improvements for the Ricci dark energy model, which they include as a demonstration even though it is already disfavored by current observations.

Load-bearing premise

The forecast rests on the simulated ten-year catalog of GW-GRB events being a faithful representation of reality: the local merger rate of 920 $Gpc^{-3}$ $yr^{-1}$, the power-law delay distribution proportional to 1/td, the Gaussian jet core angle of 4.7 degrees, and the broken-power-law GRB luminosity function together set how many standard sirens are detected and at what redshifts. If any of these astrophysical inputs is materially wrong, the reported 63-88%, 27-44%, and 55-70% improvements will not be realized.

Editorial extensions

If this is right

  • In the HDE model, the combination CBS+ET2CE in the optimistic scenario reaches sigma(H0) = 0.079 km/s/Mpc (0.12%), sigma(c) = 0.023 (2.6%), and sigma(Omega_m) = 0.0020 (0.64%), all below the 1% precision threshold for H0 and Omega_m.
  • Even in the realistic scenario, CBS+ET2CE still improves H0 to 0.14 km/s/Mpc (0.21%), c to 0.027 (3.05%), and Omega_m to 0.0023 (0.74%).
  • GW data alone, especially from ET2CE, can measure H0 with 0.18-0.64% precision in the HDE model, but gives only weak constraints on c and Omega_m, so the main role of standard sirens is breaking degeneracies rather than measuring all parameters independently.
  • The RDE model, although disfavored by current data, would also see substantial improvements, with CBS+ET2CE giving sigma(H0) = 0.097 km/s/Mpc and sigma(gamma) = 0.0036 in the optimistic scenario.
  • The actual number of standard sirens is far smaller than the often-assumed 1000 over ten years, with 252-363 in the optimistic scenario and 79-121 in the realistic scenario, so realistic event counts still deliver significant gains when combined with CBS.

Reading between the lines

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

  • The degeneracy-breaking logic is not specific to holographic dark energy: the same improvement pattern should apply to other one-extra-parameter dark energy models, since the mechanism only relies on standard sirens sampling the low-redshift distance ladder with a different degeneracy orientation than CMB and BAO data.
  • A natural extension would be to vary the local merger rate, jet opening angle, or gamma-ray burst luminosity function across their observational uncertainty ranges and recompute the improvement percentages; the paper tests optimistic versus realistic field-of-view but not the full systematic spread of these astrophysical inputs.
  • If the forecast holds, a single decade of 3G multi-messenger observations would provide a sub-percent H0 that is independent of both the CMB sound-horizon calibration and the distance-ladder calibration, which is exactly what an arbitration of the Hubble tension requires.
  • The paper's conclusion that c < 1 from CBS, implying a future big-rip singularity, would become directly testable if the tighter c constraint from CBS+ET2CE remains centered below unity, since the 2.6% precision would distinguish c = 1 (no big rip) from c < 1 at many sigma.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper forecasts cosmological parameter constraints for the holographic dark energy (HDE) and Ricci dark energy (RDE) models using mock gravitational-wave (GW) standard siren data from third-generation detectors (ET, CE, 2CE, and ET2CE) jointly with a THESEUS-like short gamma-ray burst detector. The authors simulate a 10-year catalog of binary neutron star mergers using a star-formation-rate-based merger rate with a power-law delay distribution, apply GW detectability and GRB flux thresholds, and then combine the resulting mock distance measurements with CMB+BAO+SN (CBS) data through a chi-square likelihood. The main results are that GW data alone can measure H0 to 0.2%--0.6% precision, and that adding GW data to CBS improves the constraints on H0, c, and Omega_m by 63%--88%, 27%--44%, and 55%--70% in the HDE model (with analogous improvements for RDE), thereby helping to break degeneracies left by electromagnetic data.

Significance. If the forecast is robust, it provides a concrete, quantitative case for 3G GW--GRB multi-messenger observations as a precision probe of dark energy and the Hubble tension. The paper improves on earlier work by explicitly simulating the joint GW--GRB detection process rather than assuming a fixed number of standard sirens, by considering multiple detector networks (ET, CE, 2CE, ET2CE), and by including Earth-rotation effects in the GW simulation. These are genuine methodological strengths. However, the headline improvement percentages are conditional on a set of poorly pinned astrophysical inputs (BNS merger rate, jet core angle, GRB luminosity function) and on mock data generated from the CBS best-fit model; the paper does not quantify how the results depend on those inputs. The forecast is therefore a useful demonstration of potential rather than a robust prediction, and the authors correctly note that it cannot test consistency between GW and electromagnetic data.

major comments (3)
  1. [§3.1–§3.3, Table 1] The number of simulated joint GW--GRB events (252–363 optimistic, 79–121 realistic) is controlled by several astrophysical inputs whose uncertainties are substantial: the local BNS merger rate R0 = 920 Gpc^-3 yr^-1 (Eq. 14 and Section 3.1), the power-law delay distribution P(td) = 1/td, the Gaussian jet core angle theta_c = 4.7 deg (Eq. 21), and the broken-power-law GRB luminosity function with alpha_L = -1.95, beta_L = -3, L* = 2e52 erg/s (Eq. 22). The quoted 63%–88% improvement in H0 constraints (Table 3 and Section 5) is directly tied to this event count and to the distance-error distribution, yet the paper reports no sensitivity analysis in which these inputs are varied over their plausible ranges. A factor-of-two change in R0 or theta_c, or a steeper beta_L, would substantially alter the catalog size and hence the reported improvements. The authors should either add a sensitivity study or temper the quantitative headline claims to reflect this dependence.
  2. [§4, first paragraph] The CBS baseline used for the forecast excludes the DESI 2024 BAO measurements and eBOSS DR16, even though the introduction and Section 4.5 explicitly discuss the impact of DESI 2024 on the HDE model. The paper asserts that including these datasets 'would not significantly affect' the ability of GW data to break degeneracies, but no calculation or argument is provided to support this claim. Because the reported improvement percentages are defined relative to the CBS baseline, the forecast should be re-run or at least robustly argued for a baseline that includes the DESI 2024 BAO data, which are directly relevant to the HDE model's current observational status.
  3. [§4.1] The mock GW data are generated from the CBS best-fit fiducial parameters for each model, so the combined CBS+GW analysis cannot test whether GW standard sirens are consistent with the electromagnetic dataset; the authors acknowledge this ('For the same reason, this paper does not address the consistency between GW and CBS'). This is a legitimate limitation of an error forecast, but the abstract's statement that such observations 'could be pivotal in helping solve the Hubble tension' overstates what a forecast built on a single fiducial can establish. I recommend adding an explicit caveat in the abstract or conclusions that the quoted improvements are conditional on the model and on the fiducial values being correct.
minor comments (5)
  1. [§4.2] There are repeated typos: 'givens' should be 'gives' in three places ('ET2CE (realistic) givens σ(c) = 0.220', 'CBS + ET2CE (realistic) givens σ(c) = 0.027', and 'CBS + ET2CE (realistic) givens σ(γ) = 0.0043').
  2. [§3.1, Eq. (13)] The notation in Eq. (13) is confusing: Rm(z) appears on both the left-hand side as an observer-frame rate and on the right-hand side as a source-frame rate. Please use distinct symbols, e.g., R_obs(z) and R_src(z), to avoid ambiguity.
  3. [Abstract and Tables 2–3] The abstract quotes H0 precision of '0.2–0.6%', while Tables 2 and 3 show 0.18% for ET2CE (optimistic) and 0.64% for ET (realistic) in the HDE model. Please harmonize the range, for example '0.2%–0.6%' could be revised to '0.18%–0.64%' or the abstract rounded explicitly.
  4. [§3.3] The 'realistic' scenario assumes that only about one-third of detected short GRBs provide accurate redshifts, but no reference or quantitative justification is given for this fraction. Given that it halves or more the effective sample size, a brief justification or a range of completeness fractions would strengthen the analysis.
  5. [Data Availability Statement] The Data Availability Statement reads 'Not applicable,' but the paper relies on simulated catalogs and Fisher matrix computations. Making the simulation code and catalogs available (or at least specifying the exact random seeds and software versions) would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the forecast is self-consistent and the self-referential mock-generation choice is explicitly disclosed.

full rationale

The paper's central quantitative claim is an error forecast, not a measurement or model validation. The mock GW catalog is generated at the CBS best-fit fiducial (Section 4), and the authors explicitly state that this choice means the combined CBS+GW central values remain at the CBS values and that consistency between GW and CBS is not addressed; this is a disclosed limitation of a Fisher forecast rather than a circular argument. The improvement percentages follow from adding the simulated GW Fisher information to the CBS covariance via Eqs. (24)-(28); the simulated event count and redshift distribution depend on external empirical inputs (R0, P(td), theta_c, GRB luminosity function) that are not fitted to the target result. Self-citations to the authors' previous pipeline [74] and HDE model assessment [31] are transparent methodological and motivational references, not uniqueness theorems or fitted predictions. No equation or parameter in the derivation reduces to the claimed output by construction.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central forecast rests on the HDE and RDE model equations, the Fisher matrix approximation, the 3.5PN restricted waveform, the GRB luminosity function and jet profile, and the choice to generate mock GW data from the CBS best-fit fiducial parameters. These are external inputs or modeling choices, not derived in this paper.

free parameters (6)
  • Local BNS merger rate R_m(z=0) = 920 Gpc^-3 yr^-1
    Sets the total number of simulated BNS mergers and standard sirens; adopted from O1/O2 LIGO-Virgo estimates and not varied (Section 3.1).
  • GRB luminosity function slopes and break = alpha_L=-1.95, beta_L=-3, L*=2e52 erg/s
    Controls which BNS mergers have detectable short GRB counterparts; fixed to values from Wanderman and Piran (2015), Section 3.3.
  • Jet core angle theta_c = 4.7 degrees
    Gaussian jet profile determines GRB detectability versus viewing angle; fixed to GW170817-motivated value (Section 3.3).
  • THESEUS flux threshold, duty cycle, sky coverage = PT=0.2 ph/s/cm2; 80%; 0.5
    Sets GRB detection efficiency; fixed by mission design assumptions (Section 3.3).
  • Peculiar velocity dispersion = 500 km/s
    Contributes to luminosity distance error through Eq. (26); standard adopted value (Section 3.4).
  • Redshift completeness fraction in realistic scenario = 1/3
    Defines the realistic THESEUS case, where only one-third of detected short GRBs yield redshifts through follow-up (Section 3.3).
assumptions (6)
  • domain assumption HDE model: rho_de = 3 c^2 M_pl^2 R_eh^-2 with the future event horizon as the IR cutoff (Eq. 2, Section 2.1).
    The forecast is for this model; the model is taken as the truth for simulation and is not derived or tested within this paper.
  • domain assumption RDE model: rho_de = 3 gamma M_pl^2 (Hdot + 2H^2) with Ricci scalar cutoff (Eq. 8, Section 2.2).
    The forecast is for this model; it is included as a demonstrative case although current data disfavor it.
  • domain assumption Fisher information matrix: parameter uncertainties from inverse Fisher matrix (Eq. 24, Section 3.4).
    Assumes high SNR, Gaussian posterior, and linearized waveform derivatives; standard but approximate for low-SNR events.
  • domain assumption Restricted 3.5PN inspiral waveform with stationary phase approximation (Eq. 17, Section 3.2).
    Neglects spin, tidal effects, higher harmonics, and calibration error; affects luminosity distance estimates.
  • domain assumption Short GRB Gaussian jet profile and broken power-law luminosity function (Eqs. 21-22, Section 3.3).
    Adopted from GW170817 modeling and short GRB population studies; not re-derived and not varied.
  • ad hoc to paper Mock GW data generated from the CBS best-fit fiducial parameters (Section 4, first paragraph).
    The simulated data assume the model under test is true, so the combined CBS+GW constraints are self-referential; the paper states it does not address GW-CBS consistency.

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Cite this review

Pith. "Pith review of Revisiting holographic dark energy from the perspective of multi-messenger gravitational wave astronomy: future joint observations with short gamma-ray bursts." pith.science (2026). https://pith.science/paper/IYYFQLDK

@misc{pith2026241206873,
  author       = {Pith},
  title        = {Pith review of: Revisiting holographic dark energy from the perspective of multi-messenger gravitational wave astronomy: future joint observations with short gamma-ray bursts},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IYYFQLDK}},
  note         = {Machine review of arXiv:2412.06873}
}
abstract

The advent of third-generation (3G) gravitational-wave (GW) detectors opens new opportunities for multi-messenger observations of binary neutron star merger events, holding significant potential for probing the history of cosmic expansion. In this paper, we investigate the holographic dark energy (HDE) model by using the future GW standard siren data observed from the 3G GW detectors and the short $\gamma$-ray burst THESEUS-like detector joint observations. We find that GW data alone can achieve a relatively precise estimation of the Hubble constant, with precision of $0.2\%$-$0.6\%$, but its ability to constrain other cosmological parameters remains limited. Nonetheless, since the GW data can break parameter degeneracies generated by the mainstream EM observations, CMB + BAO + SN (CBS), GW standard sirens play a crucial role in enhancing the accuracy of parameter estimation. With the addition of GW data to CBS, the constraints on cosmological parameters $H_0$, $c$ and $\Omega_{\rm{m}}$ can be improved by $63\%$-$88\%$, $27\%$-$44\%$ and $55\%$-$70\%$. In summary, observations of GW standard sirens from 3G GW detectors could be pivotal in helping solve the Hubble tension and probe the fundamental nature of dark energy.

Figures

Figures reproduced from arXiv: 2412.06873 by the authors.

Figure 1
Figure 1. Redshift distributions of BNS detected by THESEUS in synergy with ET, CE, 2CE, and ET2CE for a 10-year observation in the optimistic scenario. ET CE 2CE ET2CE Number of GW events 0 5 10 15 20 Redshift 0 1 2 3 4 [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Same as [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Distributions of luminosity distance uncertainty ∆dL/dL of GW standard sirens for ET, CE, 2CE, and ET2CE in the optimistic scenario under the HDE model. ET CE 2CE ET2CE Number of GW events 0 10 20 log10(ΔdL/dL) −2.5 −2.0 −1.5 −1.0 [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Same as [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Two-dimensional marginalized contours (68.3% and 95.4% confidence level) in the Ωm– H0 and c–H0 planes for the HDE model in the optimistic scenario using ET, CE, 2CE and ET2CE, respectively. 0.25 0.30 0.35 ­m 65 66 67 68 H0 [k m s ¡1 M p c ¡1 ] ET2CE (optimistic) CBS C…
Figure 6
Figure 6. Figure 6: Two-dimensional marginalized contours (68.3% and 95.4% confidence level) in the Ωm–H0 and c–H0 planes for the HDE model in the optimistic scenario using ET2CE, CBS and CBS + ET2CE data, respectively [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: Two-dimensional marginalized contours (68.3% and 95.4% confidence level) in the Ωm–H0 and γ–H0 planes for the RDE model in the optimistic scenario using ET2CE, CBS and CBS + ET2CE data, respectively. 0.2 0.3 0.4 ­m 65.5 66.0 66.5 67.0 H0 [k m s ¡1 M p c ¡1 ] ET2CE (rea…
Figure 8
Figure 8. Figure 8: Two-dimensional marginalized contours (68.3% and 95.4% confidence level) in the Ωm–H0 and c–H0 planes for the HDE model in the realistic and optimistic scenarios of the ET2CE data. 0.305 0.310 0.315 ­m 66.0 66.2 66.4 66.6 66.8 H0 [k m s ¡1 M p c ¡1 ] CBS+ET2CE (realist…
Figure 9
Figure 9. Figure 9: Two-dimensional marginalized contours (68.3% and 95.4% confidence level) in the Ωm–H0 and c–H0 planes for the HDE model in the realistic and optimistic scenarios of the CBS + ET2CE data [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: Two-dimensional marginalized contours (68.3% and 95.4% confidence level) in the Ωm–H0 and γ–H0 planes for the RDE model in the realistic and optimistic scenarios of the CBS + ET2CE data [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]

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Reference graph

Works this paper leans on

125 extracted references · 38 canonical work pages · cited by 2 Pith papers

  1. [74]

    A comprehensive forecast for cosmological parameter estimation using joint observations of gravitational waves and short γ-ray bursts

    Han, T.; Jin, S.J.; Zhang, J.F.; Zhang, X. A comprehensive forecast for cosmological parameter estimation using joint observations of gravitational waves and short γ-ray bursts. Eur. Phys. J. C 2024, 84, 663. https://doi.org/10.1140/epjc/s10052-024-12999-w

    work page doi:10.1140/epjc/s10052-024-12999-w 2024

  2. [1]

    Observational evidence from supernovae for an accelerating universe and a cosmological constant

    Riess, A.G.; Filippenko, A.V .; Challis, P .; Clocchiatti, A.; Diercks, A.; Garnavich, P .M.; Gilliland, R.L.; Hogan, C.J.; Jha, S.; Kirshner, R.P .; et al. Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 1998, 116, 1009–1038. https://doi.org/10.1086/300499

    doi:10.1086/300499 1998

  3. [2]

    Measurements ofΩ and Λ from 42 high redshift supernovae.Astrophys

    Perlmutter, S.; Aldering, G.; Goldhaber, G.; Knop, R.A.; Nugent, P .; Castro, P .G.; Deustua, S.; Fabbro, S.; Goobar, A.; Groom, D.E.; et al. Measurements ofΩ and Λ from 42 high redshift supernovae.Astrophys. J. 1999, 517, 565–586. https://doi.org/10.1086/307221

    doi:10.1086/307221 1999

  4. [3]

    The Case for a positive cosmological Lambda term

    Sahni, V .; Starobinsky, A.A. The Case for a positive cosmological Lambda term. Int. J. Mod. Phys. D 2000, 9, 373–444. https://doi.org/10.1142/S0218271800000542

    doi:10.1142/s0218271800000542 2000

  5. [4]

    A Phantom menace? Phys

    Caldwell, R.R. A Phantom menace? Phys. Lett. B 2002, 545, 23–29. https://doi.org/10.1016/S0370-2693(02)02589-3

    doi:10.1016/s0370-2693(02)02589-3 2002

  6. [5]

    Cosmological constant: The Weight of the vacuum

    Padmanabhan, T. Cosmological constant: The Weight of the vacuum. Phys. Rept. 2003, 380, 235–320. https://doi.org/10.1016/S0 370-1573(03)00120-0

    doi:10.1016/s0 2003

  7. [6]

    The Cosmological Constant and Dark Energy

    Peebles, P .J.E.; Ratra, B. The Cosmological Constant and Dark Energy. Rev. Mod. Phys. 2003, 75, 559–606. https://doi.org/10.110 3/RevModPhys.75.559

    2003

  8. [7]

    Dynamics of dark energy

    Copeland, E.J.; Sami, M.; Tsujikawa, S. Dynamics of dark energy. Int. J. Mod. Phys. D 2006, 15, 1753–1936. https://doi.org/10.114 2/S021827180600942X

    2006

Show all 125 references
  1. [8]

    Dark Energy.Commun

    Li, M.; Li, X.D.; Wang, S.; Wang, Y . Dark Energy.Commun. Theor. Phys.2011, 56, 525–604. https://doi.org/10.1088/0253-6102/56/3 /24

    2011 doi

  2. [9]

    Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests

    Bamba, K.; Capozziello, S.; Nojiri, S.; Odintsov, S.D. Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests. Astrophys. Space Sci. 2012, 342, 155–228. https://doi.org/10.1007/s10509-012-1181-8

    2012 doi

  3. [10]

    The Cosmological Constant Problem

    Weinberg, S. The Cosmological Constant Problem. Rev. Mod. Phys. 1989, 61, 1–23. https://doi.org/10.1103/RevModPhys.61.1

    1989 doi

  4. [11]

    The Cosmological constant

    Carroll, S.M. The Cosmological constant. Living Rev. Rel. 2001, 4, 1. https://doi.org/10.12942/lrr-2001-1

    2001 doi

  5. [12]

    A Model of holographic dark energy

    Li, M. A Model of holographic dark energy. Phys. Lett. B 2004, 603, 1. https://doi.org/10.1016/j.physletb.2004.10.014

    2004 doi

  6. [13]

    Effective field theory, black holes, and the cosmological constant

    Cohen, A.G.; Kaplan, D.B.; Nelson, A.E. Effective field theory, black holes, and the cosmological constant. Phys. Rev. Lett. 1999, 82, 4971–4974. https://doi.org/10.1103/PhysRevLett.82.4971

    1999 doi

  7. [14]

    Constraints on holographic dark energy from Type Ia supernova observations

    Zhang, X.; Wu, F.Q. Constraints on holographic dark energy from Type Ia supernova observations. Phys. Rev. D 2005, 72, 043524. https://doi.org/10.1103/PhysRevD.72.043524

    2005 doi

  8. [15]

    Constraints on Holographic Dark Energy from Latest Supernovae, Galaxy Clustering, and Cosmic Microwave Background Anisotropy Observations

    Zhang, X.; Wu, F.Q. Constraints on Holographic Dark Energy from Latest Supernovae, Galaxy Clustering, and Cosmic Microwave Background Anisotropy Observations. Phys. Rev. D 2007, 76, 023502. https://doi.org/10.1103/PhysRevD.76.023502

    2007 doi

  9. [16]

    Supernova constraints on a holographic dark energy model

    Huang, Q.G.; Gong, Y.G. Supernova constraints on a holographic dark energy model. JCAP 2004, 08, 006. https://doi.org/10.108 8/1475-7516/2004/08/006

    2004

  10. [17]

    Constraints on the dark energy from holography

    Wang, B.; Abdalla, E.; Su, R.K. Constraints on the dark energy from holography. Phys. Lett. B 2005, 611, 21–26. https: //doi.org/10.1016/j.physletb.2005.02.026

    2005 doi

  11. [18]

    Unifying phantom inflation with late-time acceleration: Scalar phantom-non-phantom transition model and generalized holographic dark energy

    Nojiri, S.; Odintsov, S.D. Unifying phantom inflation with late-time acceleration: Scalar phantom-non-phantom transition model and generalized holographic dark energy. Gen. Rel. Grav. 2006, 38, 1285–1304. https://doi.org/10.1007/s10714-006-0301-6

    2006 doi

  12. [19]

    Constraints on holographic dark energy from x-ray gas mass fraction of galaxy clusters

    Chang, Z.; Wu, F.Q.; Zhang, X. Constraints on holographic dark energy from x-ray gas mass fraction of galaxy clusters. Phys. Lett. B 2006, 633, 14–18. https://doi.org/10.1016/j.physletb.2005.10.095

    2006 doi

  13. [20]

    Holographic dark energy in a cyclic universe

    Zhang, J.f.; Zhang, X.; Liu, H.y. Holographic dark energy in a cyclic universe. Eur. Phys. J. C 2007, 52, 693–699. https: //doi.org/10.1140/epjc/s10052-007-0408-2

    2007 doi

  14. [21]

    Holographic dark energy in a Universe with spatial curvature and massive neutrinos: A full Markov Chain Monte Carlo exploration

    Li, Y.H.; Wang, S.; Li, X.D.; Zhang, X. Holographic dark energy in a Universe with spatial curvature and massive neutrinos: A full Markov Chain Monte Carlo exploration. JCAP 2013, 02, 033. https://doi.org/10.1088/1475-7516/2013/02/033

    2013 doi

  15. [22]

    Revisiting the holographic dark energy in a non-flat universe: Alternative model and cosmological parameter constraints

    Zhang, J.F.; Zhao, M.M.; Cui, J.L.; Zhang, X. Revisiting the holographic dark energy in a non-flat universe: Alternative model and cosmological parameter constraints. Eur. Phys. J. C 2014, 74, 3178. https://doi.org/10.1140/epjc/s10052-014-3178-7

    2014 doi

  16. [23]

    Holographic dark energy from minimal supergravity

    Landim, R.C.G. Holographic dark energy from minimal supergravity. Int. J. Mod. Phys. D 2016, 25, 1650050. https: //doi.org/10.1142/S0218271816500504. Universe 2025, 1, 0 18 of 22

    2016 doi

  17. [24]

    Holographic Dark Energy

    Wang, S.; Wang, Y.; Li, M. Holographic Dark Energy. Phys. Rept. 2017, 696, 1–57. https://doi.org/10.1016/j.physrep.2017.06.003

    2017 doi

  18. [25]

    Comparison of dark energy models: A perspective from the latest observational data

    Li, M.; Li, X.; Zhang, X. Comparison of dark energy models: A perspective from the latest observational data. Sci. China Phys. Mech. Astron. 2010, 53, 1631–1645. https://doi.org/10.1007/s11433-010-4083-1

    2010 doi

  19. [26]

    Comparison of dark energy models after Planck 2015

    Xu, Y.Y.; Zhang, X. Comparison of dark energy models after Planck 2015. Eur. Phys. J. C 2016, 76, 588. https://doi.org/10.1140/ epjc/s10052-016-4446-5

    2015

  20. [27]

    Reexploration of interacting holographic dark energy model: Cases of interaction term excluding the Hubble parameter

    Li, H.L.; Zhang, J.F.; Feng, L.; Zhang, X. Reexploration of interacting holographic dark energy model: Cases of interaction term excluding the Hubble parameter. Eur. Phys. J. C 2017, 77, 907. https://doi.org/10.1140/epjc/s10052-017-5473-6

    2017 doi

  21. [28]

    Exploring interacting holographic dark energy in a perturbed universe with parameterized post-Friedmann approach

    Feng, L.; Li, Y.H.; Yu, F.; Zhang, J.F.; Zhang, X. Exploring interacting holographic dark energy in a perturbed universe with parameterized post-Friedmann approach. Eur. Phys. J. C 2018, 78, 865. https://doi.org/10.1140/epjc/s10052-018-6338-3

    2018 doi

  22. [29]

    Planck Constraints on Holographic Dark Energy

    Li, M.; Li, X.D.; Ma, Y.Z.; Zhang, X.; Zhang, Z. Planck Constraints on Holographic Dark Energy. JCAP 2013, 09, 021. https://doi.org/10.1088/1475-7516/2013/09/021

    2013 doi

  23. [30]

    Theoretical aspects of holographic dark energy

    Wang, S.; Li, M. Theoretical aspects of holographic dark energy. Commun. Theor. Phys. 2023, 75, 117401. https://doi.org/10.1088/ 1572-9494/acf27c

    2023

  24. [31]

    Revisiting holographic dark energy after DESI 2024.arXiv 2024, arXiv:2411.08639v1

    Li, T.N.; Li, Y.H.; Du, G.H.; Wu, P .J.; Feng, L.; Zhang, J.F.; Zhang, X. Revisiting holographic dark energy after DESI 2024.arXiv 2024, arXiv:2411.08639v1. https://doi.org/10.48550/arXiv.2411.08639

    2024 doi arXiv

  25. [32]

    Covariant Generalized Holographic Dark Energy and Accelerating Universe

    Nojiri, S.; Odintsov, S.D. Covariant Generalized Holographic Dark Energy and Accelerating Universe. Eur. Phys. J. C 2017, 77, 528. https://doi.org/10.1140/epjc/s10052-017-5097-x

    2017 doi

  26. [33]

    Unifying Holographic Inflation with Holographic Dark Energy: A Covariant Approach

    Nojiri, S.; Odintsov, S.D.; Oikonomou, V .K.; Paul, T. Unifying Holographic Inflation with Holographic Dark Energy: A Covariant Approach. Phys. Rev. D 2020, 102, 023540. https://doi.org/10.1103/PhysRevD.102.023540

    2020 doi

  27. [34]

    Different Faces of Generalized Holographic Dark Energy

    Nojiri, S.; Odintsov, S.D.; Paul, T. Different Faces of Generalized Holographic Dark Energy. Symmetry 2021, 13, 928. https: //doi.org/10.3390/sym13060928

    2021 doi

  28. [35]

    Barrow entropic dark energy: A member of generalized holographic dark energy family

    Nojiri, S.; Odintsov, S.D.; Paul, T. Barrow entropic dark energy: A member of generalized holographic dark energy family. Phys. Lett. B 2022, 825, 136844. https://doi.org/10.1016/j.physletb.2021.136844

    2022

  29. [36]

    Holographic inflation

    Nojiri, S.; Odintsov, S.D.; Saridakis, E.N. Holographic inflation. Phys. Lett. B 2019, 797, 134829. https://doi.org/10.1016/j. physletb.2019.134829

    2019

  30. [37]

    A Holographic Dark Energy Model from Ricci Scalar Curvature

    Gao, C.; Wu, F.; Chen, X.; Shen, Y.G. A Holographic Dark Energy Model from Ricci Scalar Curvature. Phys. Rev. D 2009, 79, 043511. https://doi.org/10.1103/PhysRevD.79.043511

    2009 doi

  31. [38]

    Holographic Ricci dark energy: Current observational constraints, quintom feature, and the reconstruction of scalar-field dark energy

    Zhang, X. Holographic Ricci dark energy: Current observational constraints, quintom feature, and the reconstruction of scalar-field dark energy. Phys. Rev. D 2009, 79, 103509. https://doi.org/10.1103/PhysRevD.79.103509

    2009 doi

  32. [39]

    Holography, UV/IR Relation, Causal Entropy Bound and Dark Energy

    Cai, R.G.; Hu, B.; Zhang, Y. Holography, UV/IR Relation, Causal Entropy Bound and Dark Energy. Commun. Theor. Phys. 2009, 51, 954–960. https://doi.org/10.1088/0253-6102/51/5/39

    2009 doi

  33. [40]

    Holographic Ricci dark energy: Interacting model and cosmological constraints

    Fu, T.F.; Zhang, J.F.; Chen, J.Q.; Zhang, X. Holographic Ricci dark energy: Interacting model and cosmological constraints. Eur. Phys. J. C 2012, 72, 1932. https://doi.org/10.1140/epjc/s10052-012-1932-2

    2012 doi

  34. [41]

    Comparing holographic dark energy models with statefinder

    Cui, J.L.; Zhang, J.F. Comparing holographic dark energy models with statefinder. Eur. Phys. J. C 2014, 74, 2849. https: //doi.org/10.1140/epjc/s10052-014-2849-8

    2014 doi

  35. [42]

    Diagnosing holographic dark energy models with statefinder hierarchy

    Zhang, J.F.; Cui, J.L.; Zhang, X. Diagnosing holographic dark energy models with statefinder hierarchy. Eur. Phys. J. C 2014, 74, 3100. https://doi.org/10.1140/epjc/s10052-014-3100-3

    2014 doi

  36. [43]

    Statefinder hierarchy exploration of the extended Ricci dark energy

    Yu, F.; Cui, J.L.; Zhang, J.F.; Zhang, X. Statefinder hierarchy exploration of the extended Ricci dark energy. Eur. Phys. J. C 2015, 75, 274. https://doi.org/10.1140/epjc/s10052-015-3505-7

    2015 doi

  37. [44]

    A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−1 Mpc−1 Uncertainty from the Hubble Space Telescope and the SH0ES Team

    Riess, A.G.; Yuan, W.; Macri, L.M.; Scolnic, D.; Brout, D.; Casertano, S.; Jones, D.O.; Murakami, Y.; Anand, G.S.; Breuval, L.; et al. A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−1 Mpc−1 Uncertainty from the Hubble Space Telescope and the ...

    2022 doi

  38. [45]

    Editorial

    Cai, R.G. Editorial. Sci. China Phys. Mech. Astron. 2020, 63, 290401. https://doi.org/10.1007/s11433-020-1540-4

    2020 doi

  39. [46]

    Inflation model selection revisited after a 1.91% measurement of the Hubble constant

    Guo, R.Y.; Zhang, J.F.; Zhang, X. Inflation model selection revisited after a 1.91% measurement of the Hubble constant. Sci. China Phys. Mech. Astron. 2020, 63, 290406. https://doi.org/10.1007/s11433-019-1514-0

    2020 doi

  40. [47]

    Tale of stable interacting dark energy, observational signatures, and the H0 tension

    Yang, W.; Pan, S.; Di Valentino, E.; Nunes, R.C.; Vagnozzi, S.; Mota, D.F. Tale of stable interacting dark energy, observational signatures, and the H0 tension. JCAP 2018, 09, 019. https://doi.org/10.1088/1475-7516/2018/09/019

    2018 doi

  41. [48]

    New physics in light of the H0 tension: An alternative view

    Vagnozzi, S. New physics in light of the H0 tension: An alternative view. Phys. Rev. D 2020, 102, 023518. https://doi.org/10.110 3/PhysRevD.102.023518

    2020

  42. [49]

    Nonminimal dark sector physics and cosmological tensions

    Di Valentino, E.; Melchiorri, A.; Mena, O.; Vagnozzi, S. Nonminimal dark sector physics and cosmological tensions. Phys. Rev. D 2020, 101, 063502. https://doi.org/10.1103/PhysRevD.101.063502

    2020 doi

  43. [50]

    Interacting dark energy in the early 2020s: A promising solution to the H0 and cosmic shear tensions

    Di Valentino, E.; Melchiorri, A.; Mena, O.; Vagnozzi, S. Interacting dark energy in the early 2020s: A promising solution to the H0 and cosmic shear tensions. Phys. Dark Univ. 2020, 30, 100666. https://doi.org/10.1016/j.dark.2020.100666

    2020

  44. [51]

    Can Non-standard Recombination Resolve the Hubble Tension? Sci

    Liu, M.; Huang, Z.; Luo, X.; Miao, H.; Singh, N.K.; Huang, L. Can Non-standard Recombination Resolve the Hubble Tension? Sci. China Phys. Mech. Astron. 2020, 63, 290405. https://doi.org/10.1007/s11433-019-1509-5. Universe 2025, 1, 0 19 of 22

    2020 doi

  45. [52]

    Measuring H 0 from low-z datasets

    Zhang, X.; Huang, Q.G. Measuring H 0 from low-z datasets. Sci. China Phys. Mech. Astron. 2020, 63, 290402. https: //doi.org/10.1007/s11433-019-1504-8

    2020 doi

  46. [53]

    A gigaparsec-scale local void and the Hubble tension

    Ding, Q.; Nakama, T.; Wang, Y. A gigaparsec-scale local void and the Hubble tension. Sci. China Phys. Mech. Astron. 2020, 63, 290403. https://doi.org/10.1007/s11433-020-1531-0

    2020 doi

  47. [54]

    Testing H0 in Acoustic Dark Energy with Planck and ACT Polarization

    Lin, M.X.; Hu, W.; Raveri, M. Testing H0 in Acoustic Dark Energy with Planck and ACT Polarization. Phys. Rev. D 2020, 102, 123523. https://doi.org/10.1103/PhysRevD.102.123523

    2020 doi

  48. [55]

    Self-interacting dark matter from late decays and the H0 tension

    Hryczuk, A.; Jodłowski, K. Self-interacting dark matter from late decays and the H0 tension. Phys. Rev. D 2020, 102, 043024. https://doi.org/10.1103/PhysRevD.102.043024

    2020 doi

  49. [56]

    Chameleon dark energy can resolve the Hubble tension

    Cai, R.G.; Guo, Z.K.; Li, L.; Wang, S.J.; Yu, W.W. Chameleon dark energy can resolve the Hubble tension. Phys. Rev. D 2021, 103, 121302. https://doi.org/10.1103/PhysRevD.103.L121302

    2021 doi

  50. [57]

    Implications for the Hubble tension from the ages of the oldest astrophysical objects

    Vagnozzi, S.; Pacucci, F.; Loeb, A. Implications for the Hubble tension from the ages of the oldest astrophysical objects. JHEAp 2022, 36, 27–35. https://doi.org/10.1016/j.jheap.2022.07.004

    2022 doi

  51. [58]

    Consistency tests of ΛCDM from the early integrated Sachs-Wolfe effect: Implications for early-time new physics and the Hubble tension

    Vagnozzi, S. Consistency tests of ΛCDM from the early integrated Sachs-Wolfe effect: Implications for early-time new physics and the Hubble tension. Phys. Rev. D 2021, 104, 063524. https://doi.org/10.1103/PhysRevD.104.063524

    2021 doi

  52. [59]

    The Expansion of the Universe is Faster than Expected

    Riess, A.G. The Expansion of the Universe is Faster than Expected. Nat. Rev. Phys. 2019, 2, 10–12. https://doi.org/10.1038/s422 54-019-0137-0

    2019 doi

  53. [60]

    Tensions between the Early and the Late Universe

    Verde, L.; Treu, T.; Riess, A.G. Tensions between the Early and the Late Universe. Nature Astron. 2019, 3, 891. https: //doi.org/10.1038/s41550-019-0902-0

    2019 doi

  54. [61]

    Constraints on Interacting Dark Energy Models from the DESI Baryon Acoustic Oscillation and DES Supernovae Data

    Li, T.N.; Wu, P .J.; Du, G.H.; Jin, S.J.; Li, H.L.; Zhang, J.F.; Zhang, X. Constraints on Interacting Dark Energy Models from the DESI Baryon Acoustic Oscillation and DES Supernovae Data. Astrophys. J. 2024, 976, 1. https://doi.org/10.3847/1538-4357/ad87f0

    2024 doi

  55. [62]

    Determining the Hubble Constant from Gravitational Wave Observations

    Schutz, B.F. Determining the Hubble Constant from Gravitational Wave Observations. Nature 1986, 323, 310–311. https: //doi.org/10.1038/323310a0

    1986 doi

  56. [63]

    Using gravitational-wave standard sirens

    Holz, D.E.; Hughes, S.A. Using gravitational-wave standard sirens. Astrophys. J. 2005, 629, 15–22. https://doi.org/10.1086/4313 41

    2005 doi

  57. [64]

    Determination of Dark Energy by the Einstein Telescope: Comparing with CMB, BAO and SNIa Observations

    Zhao, W.; Van Den Broeck, C.; Baskaran, D.; Li, T.G.F. Determination of Dark Energy by the Einstein Telescope: Comparing with CMB, BAO and SNIa Observations. Phys. Rev. D 2011, 83, 023005. https://doi.org/10.1103/PhysRevD.83.023005

    2011 doi

  58. [65]

    Improving cosmological parameter estimation with the future gravitational-wave standard siren observation from the Einstein Telescope.Phys

    Zhang, X.N.; Wang, L.F.; Zhang, J.F.; Zhang, X. Improving cosmological parameter estimation with the future gravitational-wave standard siren observation from the Einstein Telescope.Phys. Rev. D 2019, 99, 063510. https://doi.org/10.1103/PhysRevD.99.063510

    2019 doi

  59. [66]

    Forecast for cosmological parameter estimation with gravitational-wave standard siren observation from the Cosmic Explorer

    Jin, S.J.; He, D.Z.; Xu, Y.; Zhang, J.F.; Zhang, X. Forecast for cosmological parameter estimation with gravitational-wave standard siren observation from the Cosmic Explorer. JCAP 2020, 03, 051. https://doi.org/10.1088/1475-7516/2020/03/051

    2020 doi

  60. [67]

    Quantifying the impacts of future gravitational-wave data on constraining interacting dark energy

    Li, H.L.; He, D.Z.; Zhang, J.F.; Zhang, X. Quantifying the impacts of future gravitational-wave data on constraining interacting dark energy. JCAP 2020, 06, 038. https://doi.org/10.1088/1475-7516/2020/06/038

    2020 doi

  61. [68]

    Probing cosmic anisotropy with gravitational waves as standard sirens.Phys

    Cai, R.G.; Liu, T.B.; Liu, X.W.; Wang, S.J.; Yang, T. Probing cosmic anisotropy with gravitational waves as standard sirens.Phys. Rev. D 2018, 97, 103005. https://doi.org/10.1103/PhysRevD.97.103005

    2018 doi

  62. [69]

    Estimating cosmological parameters by the simulated data of gravitational waves from the Einstein Telescope

    Cai, R.G.; Yang, T. Estimating cosmological parameters by the simulated data of gravitational waves from the Einstein Telescope. Phys. Rev. D 2017, 95, 044024. https://doi.org/10.1103/PhysRevD.95.044024

    2017 doi

  63. [70]

    Prospect for constraining holographic dark energy with gravitational wave standard sirens from the Einstein Telescope

    Zhang, J.F.; Dong, H.Y.; Qi, J.Z.; Zhang, X. Prospect for constraining holographic dark energy with gravitational wave standard sirens from the Einstein Telescope. Eur. Phys. J. C 2020, 80, 217. https://doi.org/10.1140/epjc/s10052-020-7767-3

    2020 doi

  64. [71]

    Taiji-TianQin-LISA network: Precisely measuring the Hubble constant using both bright and dark sirens

    Jin, S.J.; Zhang, Y.Z.; Song, J.Y.; Zhang, J.F.; Zhang, X. Taiji-TianQin-LISA network: Precisely measuring the Hubble constant using both bright and dark sirens. Sci. China Phys. Mech. Astron. 2024, 67, 220412. https://doi.org/10.1007/s11433-023-2276-1

    2024 doi

  65. [72]

    Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA

    Abbott, B.P .; Abbott, R.; Abbott, T.D.; Abraham, S.; Acernese, F.; Ackley, K.; Adams, C.; Adya, V .B.; Affeldt, C.; Agathos, M.; et al. Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA. Living Rev. Rel. 2018, 21...

    2018 doi

  66. [73]

    Synergy between CSST galaxy survey and gravitational- wave observation: Inferring the Hubble constant from dark standard sirens

    Song, J.Y.; Wang, L.F.; Li, Y.; Zhao, Z.W.; Zhang, J.F.; Zhao, W.; Zhang, X. Synergy between CSST galaxy survey and gravitational- wave observation: Inferring the Hubble constant from dark standard sirens. Sci. China Phys. Mech. Astron. 2024, 67, 230411. https://doi.org/10.100...

    2024 doi

  67. [75]

    A gravitational-wave standard siren measurement of the Hubble constant

    Abbott, B.P .; Abbott, R.; Adhikari, R.X.; Ananyeva, A.; Anderson, S.B.; Appert, S.; Arai, K.; Araya, M.C.; Barayoga, J.C.; Barish, B.C.; et al. A gravitational-wave standard siren measurement of the Hubble constant. Nature 2017, 551, 85–88. https://doi.org/10.1038/nature24471

    2017 doi

  68. [76]

    Available online: https://www.et-gw.eu (accessed on 5 March 2025)

    ET. Available online: https://www.et-gw.eu (accessed on 5 March 2025)

    2025

  69. [77]

    The Einstein Telescope: A third-generation gravitational wave observatory

    Punturo, M.; Abernathy, M.; Acernese, F.; Allen, B.; Andersson, N.; Arun, K.; Barone, F.; Barr, B.; Barsuglia, M.; Beker, M.; et al. The Einstein Telescope: A third-generation gravitational wave observatory. Class. Quant. Grav. 2010, 27, 194002. https://doi.org/10.1088/0264-93...

    2010 doi

  70. [78]

    Available online: https://cosmicexplorer.org/ (accessed on 5 March 2025)

    CE. Available online: https://cosmicexplorer.org/ (accessed on 5 March 2025)

    2025

  71. [79]

    Exploring the Sensitivity of Next Generation Gravitational Wave Detectors

    Abbott, B.P .; Abbott, R.; Abbott, T.D.; Abernathy, M.R.; Ackley, K.; Adams, C.; Addesso, P .; Adhikari, R.X.; Adya, V .B.; Affeldt, C.; et al. Exploring the Sensitivity of Next Generation Gravitational Wave Detectors. Class. Quant. Grav. 2017, 34, 044001. https://doi.org/10.1...

    2017 doi

  72. [80]

    A Horizon Study for Cosmic Explorer: Science, Observatories, and Community

    Evans, M.; Adhikari, R.X.; Afle, C.; Ballmer, S.W.; Biscoveanu, S.; Borhanian, S.; Brown, D.A.; Chen, Y.; Eisenstein, R.; Gruson, A.; et al. A Horizon Study for Cosmic Explorer: Science, Observatories, and Community. arXiv 2021, arXiv:2109.09882. https://doi.org/10.48550/arXiv...

    2021 doi arXiv

  73. [81]

    The THESEUS space mission: science goals, requirements and mission concept

    Amati, L.; O’Brien, P .T.; Götz, D.; Bozzo, E.; Santangelo, A.; Tanvir, N.; Frontera, F.; Mereghetti, S.; Osborne, J.P .; Blain, A.; et al. The THESEUS space mission: science goals, requirements and mission concept. Exper. Astron. 2021, 52, 183–218. https://doi.org/10.1007/s10...

    2021 doi

  74. [82]

    The THESEUS space mission concept: science case, design and expected performances

    Amati, L.; O’Brien, P .; Götz, D.; Bozzo, E.; Tenzer, C.; Frontera, F.; Ghirlanda, G.; Labanti, C.; Osborne, J.P .; Stratta, G.; et al. The THESEUS space mission concept: science case, design and expected performances. Adv. Space Res. 2018, 62, 191–244. https://doi.org/10.1016...

    2018 doi

  75. [83]

    THESEUS: a key space mission concept for Multi-Messenger Astrophysics

    Stratta, G.; Ciolfi, R.; Amati, L.; Bozzo, E.; Ghirlanda, G.; Maiorano, E.; Nicastro, L.; Rossi, A.; Vinciguerra, S.; Frontera, F.; et al. THESEUS: a key space mission concept for Multi-Messenger Astrophysics. Adv. Space Res. 2018, 62, 662–682. https://doi.org/10.1016/j.asr.20...

    2018 doi

  76. [84]

    THESEUS in the era of Multi-Messenger Astronomy

    Stratta, G.; Amati, L.; Ciolfi, R.; Vinciguerra, S. THESEUS in the era of Multi-Messenger Astronomy. Mem. Soc. Ast. It. 2018, 89, 205–212. https://doi.org/10.48550/arXiv.1802.01677

    2018 doi arXiv

  77. [85]

    Dimensional reduction in quantum gravity

    ’t Hooft, G. Dimensional reduction in quantum gravity. Conf. Proc. C 1993, 930308, 284–296. https://doi.org/10.48550/arXiv.gr- qc/9310026

    1993 doi

  78. [86]

    The World as a hologram

    Susskind, L. The World as a hologram. J. Math. Phys. 1995, 36, 6377–6396. https://doi.org/10.1063/1.531249

    1995 doi

  79. [87]

    Measuring the star formation rate with gravitational waves from binary black holes

    Vitale, S.; Farr, W.M.; Ng, K.; Rodriguez, C.L. Measuring the star formation rate with gravitational waves from binary black holes. Astrophys. J. Lett. 2019, 886, L1. https://doi.org/10.3847/2041-8213/ab50c0

    2019 doi

  80. [88]

    Cosmology and dark energy from joint gravitational wave-GRB observations

    Belgacem, E.; Dirian, Y.; Foffa, S.; Howell, E.J.; Maggiore, M.; Regimbau, T. Cosmology and dark energy from joint gravitational wave-GRB observations. JCAP 2019, 08, 015. https://doi.org/10.1088/1475-7516/2019/08/015

    2019 doi

  81. [89]

    Gravitational-Wave Detector Networks: Standard Sirens on Cosmology and Modified Gravity Theory

    Yang, T. Gravitational-Wave Detector Networks: Standard Sirens on Cosmology and Modified Gravity Theory. JCAP 2021, 05, 044. https://doi.org/10.1088/1475-7516/2021/05/044

    2021 doi

  82. [90]

    Cosmic Star Formation History

    Madau, P .; Dickinson, M. Cosmic Star Formation History. Ann. Rev. Astron. Astrophys. 2014, 52, 415–486. https://doi.org/10.114 6/annurev-astro-081811-125615

    2014

  83. [91]

    Are all short-hard gamma-ray bursts produced from mergers of compact stellar objects? Astrophys

    Virgili, F.J.; Zhang, B.; O’Brien, P .; Troja, E. Are all short-hard gamma-ray bursts produced from mergers of compact stellar objects? Astrophys. J. 2011, 727, 109. https://doi.org/10.1088/0004-637X/727/2/109

    2011 doi

  84. [92]

    A complete sample of bright Swift short Gamma-Ray Bursts

    D’Avanzo, P .; Salvaterra, R.; Bernardini, M.G.; Nava, L.; Campana, S.; Covino, S.; D’Elia, V .; Ghirlanda, G.; Ghisellini, G.; Melandri, A.; et al. A complete sample of bright Swift short Gamma-Ray Bursts. Mon. Not. Roy. Astron. Soc. 2014, 442, 2342–2356. https://doi.org/10.1...

    2014 doi

  85. [93]

    GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs

    Abbott, B.P .; Abbott, R.; Abbott, T.; Abraham, S.; Acernese, F.; Ackley, K.; Adams, C.; Adhikari, R.; Adya, V .; LIGO Scientific Collaboration and Virgo Collaboration; et al. GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo d...

    2019

  86. [94]

    Population of Merging Compact Binaries Inferred Using Gravitational Waves through GWTC-3

    Abbott, R.; Abbott, T.; Acernese, F.; Ackley, K.; Adams, C.; Adhikari, N.; Adhikari, R.; Adya, V .; Affeldt, C.; LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration; et al. Population of Merging Compact Binaries Inferred Using Gravitational Waves throug...

    2023 doi

  87. [95]

    Geometrical Expression for the Angular Resolution of a Network of Gravitational-Wave Detectors

    Wen, L.; Chen, Y. Geometrical Expression for the Angular Resolution of a Network of Gravitational-Wave Detectors. Phys. Rev. D 2010, 81, 082001. https://doi.org/10.1103/PhysRevD.81.082001

    2010 doi

  88. [96]

    The Last three minutes: issues in gravitational wave measurements of coalescing compact binaries

    Cutler, C.; Apostolatos, T.A.; Bildsten, L.; Finn, L.S.; Flanagan, E.E.; Kennefick, D.; Markovic, D.M.; Ori, A.; Poisson, E. The Last three minutes: issues in gravitational wave measurements of coalescing compact binaries. Phys. Rev. Lett. 1993, 70, 2984–2987. https://doi.org/...

    1993 doi

  89. [97]

    Physics, Astrophysics and Cosmology with Gravitational Waves

    Sathyaprakash, B.S.; Schutz, B.F. Physics, Astrophysics and Cosmology with Gravitational Waves. Living Rev. Rel. 2009, 12, 2. https://doi.org/10.12942/lrr-2009-2

    2009 doi

  90. [98]

    Localization accuracy of compact binary coalescences detected by the third-generation gravitational-wave detectors and implication for cosmology

    Zhao, W.; Wen, L. Localization accuracy of compact binary coalescences detected by the third-generation gravitational-wave detectors and implication for cosmology. Phys. Rev. D 2018, 97, 064031. https://doi.org/10.1103/PhysRevD.97.064031

    2018 doi

  91. [99]

    Hadamard regularization of the third post-Newtonian gravitational wave generation of two point masses

    Blanchet, L.; Iyer, B.R. Hadamard regularization of the third post-Newtonian gravitational wave generation of two point masses. Phys. Rev. D 2005, 71, 024004. https://doi.org/10.1103/PhysRevD.71.024004

    2005 doi

  92. [100]

    Gravitational Waves

    Maggiore, M. Gravitational Waves. Vol. 1: Theory and Experiments ; Oxford Master Series in Physics; Oxford University Press: Oxford, UK, 2007. Universe 2025, 1, 0 21 of 22

    2007

  93. [101]

    Joint gravitational wave—Gamma-ray burst detection rates in the aftermath of GW170817 2018

    Howell, E.J.; Ackley, K.; Rowlinson, A.; Coward, D. Joint gravitational wave—Gamma-ray burst detection rates in the aftermath of GW170817 2018. https://doi.org/10.1093/mnras/stz455

    2018 doi

  94. [102]

    The rate, luminosity function and time delay of non-Collapsar short GRBs

    Wanderman, D.; Piran, T. The rate, luminosity function and time delay of non-Collapsar short GRBs. Mon. Not. Roy. Astron. Soc. 2015, 448, 3026–3037. https://doi.org/10.1093/mnras/stv123

    2015 doi

  95. [103]

    The Brightness distribution of bursting sources in relativistic cosmologies.Astrophys

    Meszaros, P .; Meszaros, A. The Brightness distribution of bursting sources in relativistic cosmologies.Astrophys. J. 1995, 449, 9–16. https://doi.org/10.1086/176026

    1995 doi

  96. [104]

    Cosmological effects on the observed flux and fluence distributions of gamma-ray bursts: Are the most distant bursts in general the faintest ones? Astron

    Meszaros, A.; Ripa, J.; Ryde, F. Cosmological effects on the observed flux and fluence distributions of gamma-ray bursts: Are the most distant bursts in general the faintest ones? Astron. Astrophys. 2011, 529, A55. https://doi.org/10.1051/0004-6361/201014918

    2011 doi

  97. [105]

    Comparison of the gamma-ray burst sensitivity of different detectors

    Band, D.L. Comparison of the gamma-ray burst sensitivity of different detectors. Astrophys. J. 2003, 588, 945–951. https: //doi.org/10.1086/374242

    2003 doi

  98. [106]

    Reducing the weak lensing noise for the gravitational wave Hubble diagram using the non-Gaussianity of the magnification distribution

    Hirata, C.M.; Holz, D.E.; Cutler, C. Reducing the weak lensing noise for the gravitational wave Hubble diagram using the non-Gaussianity of the magnification distribution. Phys. Rev. D 2010, 81, 124046. https://doi.org/10.1103/PhysRevD.81.124046

    2010 doi

  99. [107]

    Science with the space-based interferometer eLISA

    Tamanini, N.; Caprini, C.; Barausse, E.; Sesana, A.; Klein, A.; Petiteau, A. Science with the space-based interferometer eLISA. III: Probing the expansion of the Universe using gravitational wave standard sirens. JCAP 2016, 04, 002. https://doi.org/10.1088/14 75-7516/2016/04/002

    2016 doi

  100. [108]

    Testing the Quasar Hubble Diagram with LISA Standard Sirens

    Speri, L.; Tamanini, N.; Caldwell, R.R.; Gair, J.R.; Wang, B. Testing the Quasar Hubble Diagram with LISA Standard Sirens. Phys. Rev. D 2021, 103, 083526. https://doi.org/10.1103/PhysRevD.103.083526

    2021 doi

  101. [109]

    Finding the electromagnetic counterparts of cosmological standard sirens

    Kocsis, B.; Frei, Z.; Haiman, Z.; Menou, K. Finding the electromagnetic counterparts of cosmological standard sirens. Astrophys. J. 2006, 637, 27–37. https://doi.org/10.1086/498236

    2006 doi

  102. [110]

    Accurate method to determine the systematics due to the peculiar velocities of galaxies in measuring the Hubble constant from gravitational-wave standard sirens

    He, J.H. Accurate method to determine the systematics due to the peculiar velocities of galaxies in measuring the Hubble constant from gravitational-wave standard sirens. Phys. Rev. D 2019, 100, 023527. https://doi.org/10.1103/PhysRevD.100.023527

    2019 doi

  103. [111]

    Distance Priors from Planck Final Release

    Chen, L.; Huang, Q.G.; Wang, K. Distance Priors from Planck Final Release. JCAP 2019, 02, 028. https://doi.org/10.1088/1475-7 516/2019/02/028

    2019 doi

  104. [112]

    The 6dF Galaxy Survey: Baryon Acoustic Oscillations and the Local Hubble Constant

    Beutler, F.; Blake, C.; Colless, M.; Jones, D.H.; Staveley-Smith, L.; Campbell, L.; Parker, Q.; Saunders, W.; Watson, F. The 6dF Galaxy Survey: Baryon Acoustic Oscillations and the Local Hubble Constant. Mon. Not. Roy. Astron. Soc. 2011, 416, 3017–3032. https://doi.org/10.1111...

    2011

  105. [113]

    The clustering of the SDSS DR7 main Galaxy sample – I

    Ross, A.J.; Samushia, L.; Howlett, C.; Percival, W.J.; Burden, A.; Manera, M. The clustering of the SDSS DR7 main Galaxy sample – I. A 4 per cent distance measure at z = 0.15. Mon. Not. Roy. Astron. Soc. 2015, 449, 835–847. https://doi.org/10.1093/mnras/stv154

    2015 doi

  106. [114]

    The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample

    Alam, S.; Ata, M.; Bailey, S.; Beutler, F.; Bizyaev, D.; Blazek, J.A.; Bolton, A.S.; Brownstein, J.R.; Burden, A.; Chuang, C.; et al. The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample. ...

    2017 doi

  107. [115]

    The Pantheon+ Analysis: Cosmological Constraints

    Brout, D.; Scolnic, D.; Popovic, B.; Riess, A.G.; Carr, A.; Zuntz, J.; Kessler, R.; Davis, T.M.; Hinton, S.; Jones, D.; et al. The Pantheon+ Analysis: Cosmological Constraints. Astrophys. J. 2022, 938, 110. https://doi.org/10.3847/1538-4357/ac8e04

    2022 doi

  108. [116]

    Available online: https://www.et-gw.eu/index.php/etsensitivities/ (accessed on 5 March 2025)

    2025

  109. [117]

    Available online: https://cosmicexplorer.org/sensitivity.html (accessed on 5 March 2025)

    2025

  110. [118]

    Kilonovae and Optical Afterglows from Binary Neutron Star Mergers

    Zhu, J.P .; Wu, S.; Yang, Yu.; Liu, C.; Zhang, B.; Song, H.; Gao, H.; Cao, Z.; Yu, Y.; Kang, Y.; et al. Kilonovae and Optical Afterglows from Binary Neutron Star Mergers. II. Optimal Search Strategy for Serendipitous Observations and Target-of-opportunity Observations of Gravi...

    2023 doi

  111. [119]

    DESI 2024 III: Baryon Acoustic Oscillations from Galaxies and Quasars

    Adame, A.G.; Aguilar, J.; Ahlen, S.; Alam, S.; Alexander, D.M.; Alvarez, M.; Alves, O.; Anand, A.; Andrade, U.; Armengaud, E.; et al. DESI 2024 III: Baryon Acoustic Oscillations from Galaxies and Quasars. arXiv 2024, arXiv:2404.03000. https: //doi.org/10.48550/arXiv.2404.03000

    2024 doi arXiv

  112. [120]

    DESI 2024 IV: Baryon Acoustic Oscillations from the Lyman Alpha Forest

    Adame, A.G.; Aguilar, J.; Ahlen, S.; Alam, S.; Alexander, D.M.; Alvarez, M.; Alves, O.; Anand, A.; Andrade, U.; Armengaud, E.; et al. DESI 2024 IV: Baryon Acoustic Oscillations from the Lyman Alpha Forest. arXiv 2024, arXiv:2404.03001. https: //doi.org/10.1088/1475-7516/2025/01/124

    2024 arXiv

  113. [121]

    The 16th Data Release of the Sloan Digital Sky Surveys: First Release from the APOGEE-2 Southern Survey and Full Release of eBOSS Spectra

    Ahumada, R.; Prieto, C.A.; Almeida, A.; Anders, F.; Anderson, S.F.; Andrews, B.H.; Anguiano, B.; Arcodia, R.; Armengaud, E.; Aubert, M.; et al. The 16th Data Release of the Sloan Digital Sky Surveys: First Release from the APOGEE-2 Southern Survey and Full Release of eBOSS Spe...

    2020 doi

  114. [122]

    The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample

    Scolnic, D.M.; Jones, D.O.; Rest, A.; Pan, Y.C.; Chornock, R.; Foley, R.J.; Huber, M.E.; Kessler, R.; Narayan, G.; Riess, A.G.; et al. The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon...

    2018 doi

  115. [123]

    Measurement of Quantum Fluctuations in Geometry

    Hogan, C.J. Measurement of Quantum Fluctuations in Geometry. Phys. Rev. D 2008, 77, 104031. https://doi.org/10.1103/ PhysRevD.77.104031. Universe 2025, 1, 0 22 of 22

    2008

  116. [124]

    Indeterminacy of Holographic Quantum Geometry

    Hogan, C.J. Indeterminacy of Holographic Quantum Geometry. Phys. Rev. D 2008, 78, 087501. https://doi.org/10.1103/ PhysRevD.78.087501

    2008

  117. [125]

    Available online: https://www.esa.int/Science_Exploration/Space_Science/Integral_challenges_physics_beyond_Einstein (ac- cessed on 5 March 2025). Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual aut...

    2025

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