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Determination of cosmic curvature independent of the sound horizon and $H_0$ using BOSS/eBOSS and DESI DR1 BAO observations

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Pith's one-line read A model-independent, sound-horizon-free and $H_0$-free curvature measurement finds the universe spatially flat within $1\sigma$.

desk verdict Incremental but honest application of an existing sound-horizon-free curvature test to DESI DR1; the central flat-universe result is plausible, but the quoted precision rests on an incomplete covariance treatment. read the letter →

arxiv 2411.14154 v1 pith:FFK3NPVB submitted 2024-11-21 astro-ph.CO

Tonghua Liu , Shengjia Wang , Hengyu Wu , Jieci Wang This is my paper · ORCID
classification astro-ph.CO
keywords cosmiccurvaturebaryonacousticoscillationschronometersGaussianprocessartificialneuralnetworkspatialflatnessmodel-independentcosmologyDESIDR1
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

The paper's goal is a measurement of the spatial curvature of the universe that does not lean on any cosmological model, on the sound-horizon ruler $r_d$, or on the Hubble constant $H_0$. It combines transverse and line-of-sight BAO measurements from BOSS/eBOSS and DESI DR1 with Hubble-parameter values from cosmic chronometers, reconstructing the expansion history twice: once with Gaussian processes and once with artificial neural networks. When all BAO data are combined, the Gaussian-process pipeline gives $\Omega_K=-0.040^{+0.142}_{-0.145}$ and the ANN pipeline gives $\Omega_K=-0.010^{+0.405}_{-0.424}$, both consistent with a spatially flat universe at $1\sigma$. A sympathetic reader should care because this is one of the few curvature constraints that is independent of early-universe physics and of model-dependent assumptions, so it can test the standard cosmological model from late-universe geometry alone.

What carries the argument

The central object is the ratio identity in Eq. (2): $[D_A(z)]_{\mathrm{BAO+CC}} = \frac{c}{(1+z)[H(z)]_{\mathrm{CC}}} \left(\frac{D_M/r_d}{D_H/r_d}\right)_{\mathrm{BAO}}$, in which $r_d$ disappears. This converts BAO measurements into absolute distances using only the cosmic-chronometer $H(z)$ reconstruction. To build that reconstruction, the paper uses the 32 CC $H(z)$ points with two non-parametric methods: Gaussian processes with a Matérn($\nu=9/2$) kernel, and an artificial neural network. The curvature then enters through the FLRW distance relation Eq. (7), and the fit is performed by maximizing the likelihood in Eq. (8), whose covariance matrix includes the reconstruction errors and a local cross-covariance term between the two distance estimators.

What would settle it

Recompute the $\Omega_K$ posterior propagating the full covariance of the reconstructed $H(z)$, including off-diagonal terms between different redshifts, rather than the diagonal-plus-local approximation in Eq. (8); if the error bars widen beyond roughly $0.14$ in the Gaussian-process case, the paper's precision claim would be undermined. A complementary check is to run the same pipeline on mock BAO and cosmic-chronometer catalogs with known nonzero $\Omega_K$ and see whether the $1\sigma$ intervals recover the input value at the expected rate.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that the sound horizon cancels exactly if one divides the transverse BAO distance $D_M/r_d$ by the line-of-sight BAO distance $D_H/r_d$, leaving $D_M/D_H$; multiplying by the cosmic-chronometer Hubble parameter converts this into an absolute angular diameter distance $[D_A]_{\mathrm{BAO+CC}}$. Comparing these distances with the curved-geometry relation $D_A(z;\Omega_K)$ obtained from the reconstructed comoving distance yields a one-parameter likelihood for $\Omega_K$. The combined BOSS/eBOSS plus DESI DR1 sample gives $\Omega_K=-0.040^{+0.142}_{-0.145}$ with Gaussian-process reconstruction, the tightest result in the paper ($\Delta\Omega_K\simeq0.14$); the ANN reconstruction gives a consistent but much looser $-0.010^{+0.405}_{-0.424}$. The paper reads this as evidence that the late universe is spatially flat within $1\sigma$, and that the two data sources and two reconstruction methods agree in their central values even though their precisions differ.

Load-bearing premise

That the reconstructed $H(z)$ curve from cosmic chronometers is accurate everywhere in the fitted redshift range, and that correlations between its error bars at different redshifts are small enough to ignore when computing the quoted $\Omega_K$ uncertainties.

Editorial extensions

If this is right

  • If the result holds, a flat late-universe geometry is established without assuming $\Lambda$CDM, using only BAO and clock measurements.
  • The cancellation of $r_d$ gives future BAO surveys a way to report absolute distances without waiting for a model-dependent sound-horizon calibration.
  • Because $H_0$ cancels out of the ratio, the curvature constraint would not shift if the Hubble tension is resolved by changing the early-universe $H_0$.
  • The roughly $\sqrt{N}$ improvement in precision means ongoing DESI observations and more cosmic-chronometer data should tighten $\Omega_K$ toward the few-percent level.
  • The method needs no distance-duality assumption, so any future inconsistency between this curvature value and one from standard candles would point to new physics or systematics.

Reading between the lines

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

  • The paper does not propagate the full off-diagonal covariance of the reconstructed $H(z)$; if that covariance is sizable, the claimed precision advantage over earlier work could shrink.
  • The sign difference between the DESI (slightly positive) and BOSS/eBOSS (slightly negative) central values might reflect per-sample systematics rather than cosmic geometry; combining the samples could hide such systematics.
  • The same ratio construction could be applied to future high-redshift BAO measurements to test whether the flat conclusion persists beyond the current $z\simeq2.3$ range.
  • An independent cross-check would be to replace the cosmic-chronometer $H(z)$ with model-independent $H(z)$ from other clocks, such as strong-lensing time delays, to test whether the reconstruction method drives the result.
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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. This paper proposes a method to measure the cosmic curvature Omega_K using BAO observations from BOSS/eBOSS and DESI DR1 together with cosmic-chronometer H(z) data, without calibrating the BAO sound horizon and without assuming a specific cosmological model. The method reconstructs H(z) from cosmic chronometers with Gaussian process (GP) and artificial neural network (ANN) techniques, uses the BAO transverse and line-of-sight ratios to obtain absolute angular diameter distances via Eq. (2), and fits Omega_K through Eq. (8) with the FLRW distance relation. The authors report Omega_K = -0.040^{+0.142}_{-0.145} (GP) and Omega_K = -0.010^{+0.405}_{-0.424} (ANN) for the combined BOSS/eBOSS plus DESI DR1 sample, concluding that the late universe is spatially flat within 1 sigma and that the GP constraint is more precise than recent similar measurements.

Significance. If correct, this work provides a late-universe curvature measurement that is independent of the sound-horizon scale, H0, and any assumed dark-energy or cosmological model, which makes it a useful cross-check of Planck-based flatness conclusions. The central flatness result is likely robust: the reported central values are close to zero and the quoted uncertainties are large enough that even a moderate increase in the error budget would not move the constraint away from flatness at the 1-sigma level. The paper also makes a constructive comparison between GP and ANN reconstruction methods and shows that the two give consistent central values. The main limitation is that the quantitative precision claim rests on a covariance treatment that appears incomplete, so the specific improvement over previous work is not yet established.

major comments (3)
  1. [II.C, Eq. (8)] The covariance matrix used in the likelihood does not propagate the off-diagonal correlations of the reconstructed H(z). Both [DA]BAO+CC in Eq. (2) and [DA]CC through DC(z) in Eqs. (5)-(7) are constructed from the same GP or ANN posterior for H_CC(z). Because the Matérn kernel in Eq. (4) has a finite correlation length, Cov([DA]BAO+CC_i, [DA]BAO+CC_j) and Cov([DA]CC_i, [DA]CC_j) are nonzero for i != j, and there are also cross-correlations between the two distance estimates. The paper adds only diagonal statistical errors (Covstat_ii) plus a local cross-covariance term Covcorr_ij, which as written is not the full covariance of the data vector Delta D. If the omitted terms are positive, the quoted 1-sigma intervals (e.g., Omega_K = -0.040^{+0.142}_{-0.145} in Sec. III) are underestimated, and the claim in Sec. IV that the precision surpasses recent measurements is not established. Please propagate the full GP/ANN posterior covariance into Eq. (8), including the covariance of the integrated DC(z), or provide a mock-based demonstration that the neglected off-diagonal correlations are negligible.
  2. [II.C (H0-independence claim)] The statement that the result is independent of H0 is supported only by an undocumented test. Since [DA]BAO+CC in Eq. (2) has no explicit H0 dependence while [DA]CC in Eq. (7) depends on H0 through the distance formula, varying H0 as a free parameter while keeping the reconstructed H_CC(z) fixed will in general change Delta D and hence the inferred Omega_K. The cancellation the authors describe requires that H0 and the entire reconstructed H_CC(z) curve rescale together, which is not a property of the likelihood as written. Please provide either an explicit derivation of the invariance or a figure showing that the Omega_K posterior is stable over a wide range of adopted H0 priors.
  3. [II.A and Table I] The BAO measurements are treated as independent: Table I quotes only diagonal errors for DM/rd and DH/rd. Published BOSS/eBOSS and DESI DR1 analyses provide full covariance matrices that include correlations between redshift bins and between the transverse and line-of-sight distance measurements. Because the precision claim in Sec. IV depends on the total error budget, the authors should either incorporate the full BAO covariance matrices or justify quantitatively that the off-diagonal elements are negligible for the combination considered here.
minor comments (5)
  1. [Sec. III vs Sec. IV] The text in Sec. III says the precision 'is not exceptionally high compared to previous work,' but Sec. IV states that the GP precision 'surpasses recent measurements'; these statements should be reconciled with a direct comparison of the quoted error bars.
  2. [Abstract and Table II] The ANN combined result is quoted with an upper error of 0.424 in the Abstract and 0.427 in Table II; the numbers should be made consistent.
  3. [Eq. (4) and surrounding text] The text describes the kernel as the 'squared exponential form,' but Eq. (4) is the Matérn covariance with nu = 9/2; please correct the wording.
  4. [II.C] The phrase 'the distance duality relation relation' has a duplicated word and should be corrected.
  5. [II.B (ANN)] The ANN architecture choice (single hidden layer with 4096 neurons) is justified only by reference to a code repository; a brief discussion of why this architecture is appropriate for the present data would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No constructional circularity: the curvature parameter is a fitted target, not an input, and the shared H(z) reconstruction enters as a statistical covariance issue rather than a definitional reduction.

full rationale

Walking the derivation chain, the paper does not define the target quantity in terms of itself and does not rename a fit as a prediction. The BAO ratios DM/rd and DH/rd enter Eq. (2) only through the rd-independent combination DM/DH; the CC data are reconstructed into H(z) by GP or ANN independently of the cosmological fit, and the hyperparameter optimization is explicitly performed separately from the cosmological-parameter fitting. The comoving distance DC(z) is obtained by integrating the reconstructed H(z) in Eq. (5), and the angular diameter distance model in Eq. (7) is then compared with the BAO+CC angular diameter distances through the likelihood in Eq. (8). The parameter ΩK is a free parameter sampled by MCMC; it is not set by the reconstruction and no fitted value is later presented as a prediction of the method. The main statistical concern raised about the analysis, namely that the same reconstructed H(z) appears in both the BAO+CC 'observed' distances and the model distances, is a real error-propagation and covariance-modeling issue, but it is not a circular step: the paper explicitly acknowledges the shared reconstruction and includes a cross-covariance term Covcorr, and the completeness of that covariance matrix affects uncertainty estimates rather than making the derivation equivalent to its inputs by construction. The few self-citations in the paper are contextual or methodological comparisons and are not load-bearing; the kernel choice is attributed to Seikel & Clarkson and the ANN architecture to Wang et al., which are independent references. No uniqueness theorem or author-imported ansatz is used to force the result. The stated limitations, such as not extrapolating beyond the redshift range, broader ANN uncertainties, and modest precision, do not indicate circularity. Therefore no circular step can be exhibited from the manuscript text.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central constraint rests on standard cosmological assumptions (FLRW, shared BAO ruler, unbiased chronometers) and on the specific reconstruction choices (GP kernel and ANN architecture). No new particles or entities are introduced. The main unquantified risks are the covariance treatment and the asserted H0 independence.

free parameters (2)
  • GP kernel hyperparameters (sigma_f and length scale l)
    Optimized by marginal likelihood on the 32 CC H(z) points. The choice of kernel and hyperparameters determines the smoothness and uncertainty of the reconstructed H(z), which directly propagates into DA and DC, and hence into Omega_K.
  • ANN architecture and training hyperparameters (single hidden layer, 4096 neurons) = 4096 neurons in one hidden layer
    Taken from Wang et al. (2020) without reoptimization. The ANN reconstruction of H(z) is the second input to the curvature fit and produces a significantly larger uncertainty on Omega_K, so the architecture choice is a load-bearing modeling assumption.
assumptions (5)
  • domain assumption FLRW metric and the distance-redshift relation in Eq. (7) hold at all redshifts used.
    The curvature constraint compares the BAO+CC angular diameter distance to the model DA(z; Omega_K) from Eq. (7). If the true spacetime is not FLRW or the distance relation is modified, the estimated Omega_K is not the spatial curvature.
  • domain assumption BAO transverse and line-of-sight measurements at a given effective redshift share the same sound horizon rd, so rd cancels in the ratio DM/DH.
    Used in Eq. (2). The cancellation is valid only if both directions probe the same standard ruler and the effective redshifts are identical; minor mismatch would reintroduce a dependence on rd.
  • domain assumption Cosmic chronometer H(z) measurements are unbiased standard clocks with known errors.
    The 32 CC points are the only absolute calibration for distances. Unmodeled systematics in the differential-age method would shift both DA and DC, biasing Omega_K.
  • ad hoc to paper The chosen GP kernel (Matérn nu=9/2) and the ANN architecture give unbiased reconstructions of H(z).
    The reconstructed curves enter both distance estimates. The paper does not validate the reconstructions against independent H(z) probes or simulated mocks, so the fidelity of the smooth curves is an unproven modeling input.
  • ad hoc to paper The Hubble constant H0, taken from the reconstructed H(z=0), does not affect the Omega_K constraint.
    The paper asserts that tests show H0 has no effect, but does not present these tests. Since H0 appears in Eq. (7), this cancellation is not demonstrated transparently.

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Cite this review

Pith. "Pith review of Determination of cosmic curvature independent of the sound horizon and $H_0$ using BOSS/eBOSS and DESI DR1 BAO observations." pith.science (2026). https://pith.science/paper/FFK3NPVB

@misc{pith2026241114154,
  author       = {Pith},
  title        = {Pith review of: Determination of cosmic curvature independent of the sound horizon and $H_0$ using BOSS/eBOSS and DESI DR1 BAO observations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FFK3NPVB}},
  note         = {Machine review of arXiv:2411.14154}
}
abstract

We present an improved model-independent method for determining the cosmic curvature using the observations of Baryon Acoustic Oscillations (BAOs) and the Hubble parameter. The purpose of this work is to provide insights into late-universe curvature measurements using available observational data and techniques. Thus, we use two sources of BAO data sets, BOSS/eBOSS and latest DESI DR1, and two reconstruction methods, Gaussian process (GP) and artificial neural network (ANN). It is important to highlight that our method circumvents influence induced by the sound horizon in BAO observations and the Hubble constant. Combining BAO data from BOSS/eBOSS plus DESI DR1, we find that the constraint on the cosmic curvature results in $\Omega_K=-0.040^{+0.142}_{-0.145}$ with an observational uncertainty of $1\sigma$ in the framework of GP method. This result changes to $\Omega_K=-0.010^{+0.405}_{-0.424}$ when the ANN method is applied. Further comparative analysis of samples from two BAO data sources, we find that there is almost no difference between the two samples. Although the curvature values obtained from the data samples using DESI DR1 are on the slightly positive and the samples using BOSS/eBOSS are on the slightly negative, these results both report that our universe has a flat spatial curvature within uncertainties, and the precision of constraining the curvature with two BAO samples is almost equal.

Figures

Figures reproduced from arXiv: 2411.14154 by the authors.

Figure 1
Figure 1. FIG. 1: Left: The reconstructions of [ [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Same as the Fig. 1 but using ANN method. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

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Forward citations

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Reference graph

Works this paper leans on

74 extracted references · 11 canonical work pages · cited by 3 Pith papers

  1. [1]

    2021, Phys

    Handley, W. 2021, Phys. Rev. D , 103, L041301. doi:10.1103/PhysRevD.103.L041301

    doi:10.1103/physrevd.103.l041301 2021

  2. [2]

    A., Akarsu, ¨O., et al

    Di Valentino, E., Anchordoqui, L. A., Akarsu, ¨O., et al. 2021, Astroparticle Physics, 131, 102605. doi:10.1016/j.astropartphys.2021.102605

    arXiv 2021

  3. [3]

    2020, Astron

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

    doi:10.1051/0004- 2020

  4. [4]

    2020, Nature Astronomy, 4, 196

    Di Valentino, E., Melchiorri, A., & Silk, J. 2020, Nature Astronomy, 4, 196. doi:10.1038/s41550-019-0906-9

    doi:10.1038/s41550-019-0906-9 2020

  5. [5]

    L., Karwal, T., et al

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

    doi:10.1103/physrevlett.122.221301 2019

  6. [6]

    M., Peiris, H

    Feeney, S. M., Peiris, H. V., Williamson, A. R., et al. 2019, Phys. Rev. Lett. , 122, 061105. doi:10.1103/PhysRevLett.122.061105

    doi:10.1103/physrevlett.122.061105 2019

  7. [8]

    2022, Astron

    Liu, T., Cao, S., Li, X., et al. 2022, Astron. Astrophys., 668, A51. doi:10.1051/0004-6361/202243375

    doi:10.1051/0004-6361/202243375 2022

  8. [9]

    E., et al

    Liao, K., Shafieloo, A., Keeley, R. E., et al. 2020, Astro- phys. J. Lett., 895, L29. doi:10.3847/2041-8213/ab8dbb

    doi:10.3847/2041-8213/ab8dbb 2020

Show all 74 references
  1. [10]

    G., Bargiacchi, G., Bogdan, M., et al

    Dainotti, M. G., Bargiacchi, G., Bogdan, M., et al. 2023, arXiv:2303.06974. doi:10.48550/arXiv.2303.06974

    2023 doi arXiv

  2. [11]

    L., Bargiacchi, G., Dainotti, M

    Lenart, A. L., Bargiacchi, G., Dainotti, M. G., et al. 2023, Astrophys. J., Suppl. Ser., 264, 46. doi:10.3847/1538- 4365/aca404

    2023 doi

  3. [12]

    G., De Simone, B

    Dainotti, M. G., De Simone, B. D., Schiavone, T., et al. 2022, Galaxies, 10, 24. doi:10.3390/galaxies10010024

    2022 doi

  4. [13]

    2023, Phys

    Qi, J.-Z., Meng, P., Zhang, J.-F., et al. 2023, Phys. Rev. D , 108, 063522. doi:10.1103/PhysRevD.108.063522

    2023 doi

  5. [14]

    2021, Astrophys

    Vagnozzi, S., Loeb, A., & Moresco, M. 2021, Astrophys. J. , 908, 84. doi:10.3847/1538-4357/abd4df

    2021 doi

  6. [15]

    & Anchordoqui, L

    Zuckerman, E. & Anchordoqui, L. A. 2022, Journal of High Energy Astrophysics, 33, 10. doi:10.1016/j.jheap.2021.10.002

    2022 doi

  7. [16]

    Dinda, B. R. 2022, Phys. Rev. D , 105, 063524. doi:10.1103/PhysRevD.105.063524

    2022 doi

  8. [17]

    2019, Phys

    Collett, T., Montanari, F., & R¨ as¨ anen, S. 2019, Phys. Rev. Lett. , 123, 231101. doi:10.1103/PhysRevLett.123.231101

    2019 doi

  9. [18]

    & Melia, F

    Wei, J.-J. & Melia, F. 2020, Astrophys. J. , 897, 127. doi:10.3847/1538-4357/ab959b

    2020 doi

  10. [19]

    2021, Mon

    Qi, J.-Z., Zhao, J.-W., Cao, S., et al. 2021, Mon. Not. Roy. Astron. Soc., 503, 2179. doi:10.1093/mnras/stab638

    2021 doi

  11. [20]

    2022, Astrophys

    Liu, T., Cao, S., Biesiada, M., et al. 2022, Astrophys. J. , 939, 37. doi:10.3847/1538-4357/ac93f3

    2022 doi

  12. [21]

    2023, Phys

    de Cruz P´ erez, J., Park, C.-G., & Ratra, B. 2023, Phys. Rev. D , 107, 063522. doi:10.1103/PhysRevD.107.063522

    2023 doi

  13. [22]

    2023, Mon

    Favale, A., G´ omez-Valent, A., & Migliaccio, M. 2023, Mon. Not. Roy. Astron. Soc., 523, 3406. 8 doi:10.1093/mnras/stad1621

    2023 doi

  14. [23]

    2021, Mon

    Dhawan, S., Alsing, J., & Vagnozzi, S. 2021, Mon. Not. Roy. Astron. Soc., 506, L1. doi:10.1093/mnrasl/slab058

    2021 doi

  15. [24]

    G., Ghosh, A., & Koopmans, L

    Mertens, F. G., Ghosh, A., & Koopmans, L. V. E. 2018, Mon. Not. Roy. Astron. Soc., 478, 3640. doi:10.1093/mnras/sty1207

    2018 doi

  16. [25]

    L., & Mifsud, J

    Mukherjee, P., Said, J. L., & Mifsud, J. 2022, JCAP, 2022, 029. doi:10.1088/1475-7516/2022/12/029

    2022 doi

  17. [26]

    Colg´ ain, E. ´O. & Sheikh-Jabbari, M. M. 2021, arXiv:2101.08565. doi:10.48550/arXiv.2101.08565

    2021 doi arXiv

  18. [27]

    1972, Gravitation and Cosmology: Princi- ples and Applications of the General Theory of Relativ- ity, by Steven Weinberg, pp

    Weinberg, S. 1972, Gravitation and Cosmology: Princi- ples and Applications of the General Theory of Relativ- ity, by Steven Weinberg, pp. 688. ISBN 0-471-92567-5. Wiley-VCH , July 1972., 688

    1972

  19. [28]

    J., Zehavi, I., Hogg, D

    Eisenstein, D. J., Zehavi, I., Hogg, D. W., et al. 2005, Astrophys. J. , 633, 560. doi:10.1086/466512

    2005 doi

  20. [29]

    J., Peacock, J

    Cole, S., Percival, W. J., Peacock, J. A., et al. 2005, Mon. Not. Roy. Astron. Soc., 362, 505. doi:10.1111/j.1365- 2966.2005.09318.x

    2005

  21. [30]

    2011, Mon

    Beutler, F., Blake, C., Colless, M., et al. 2011, Mon. Not. Roy. Astron. Soc., 416, 3017. doi:10.1111/j.1365- 2966.2011.19250.x

    2011

  22. [31]

    2017, Mon

    Alam, S., Ata, M., Bailey, S., et al. 2017, Mon. Not. Roy. Astron. Soc., 470, 2617. doi:10.1093/mnras/stx721

    2017 doi

  23. [32]

    2021, Phys

    Alam, S., Aubert, M., Avila, S., et al. 2021, Phys. Rev. D , 103, 083533. doi:10.1103/PhysRevD.103.083533

    2021 doi

  24. [33]

    2012, Mon

    Blake, C., Brough, S., Colless, M., et al. 2012, Mon. Not. Roy. Astron. Soc., 425, 405. doi:10.1111/j.1365- 2966.2012.21473.x

    2012

  25. [34]

    2021, Classi- cal and Quantum Gravity, 38, 153001

    Di Valentino, E., Mena, O., Pan, S., et al. 2021, Classi- cal and Quantum Gravity, 38, 153001. doi:10.1088/1361- 6382/ac086d

    2021 doi

  26. [35]

    F., Aboubrahim, A., et al

    Abdalla, E., Abell´ an, G. F., Aboubrahim, A., et al. 2022, Journal of High Energy Astrophysics, 34, 49. doi:10.1016/j.jheap.2022.04.002

    2022 doi

  27. [36]

    & Skara, F

    Perivolaropoulos, L. & Skara, F. 2022, New Astronomy Reviews, 95, 101659. doi:10.1016/j.newar.2022.101659

    2022

  28. [37]

    E., Paviot, R., Vargas Maga˜ na, M., et al

    Bautista, J. E., Paviot, R., Vargas Maga˜ na, M., et al. 2021, Mon. Not. Roy. Astron. Soc., 500, 736. doi:10.1093/mnras/staa2800

    2021 doi

  29. [38]

    E., Paviot, R., et al

    Gil-Mar ´ ın, H., Bautista, J. E., Paviot, R., et al. 2020, Mon. Not. Roy. Astron. Soc., 498, 2492. doi:10.1093/mnras/staa2455

    2020 doi

  30. [39]

    2020, Mon

    Tamone, A., Raichoor, A., Zhao, C., et al. 2020, Mon. Not. Roy. Astron. Soc., 499, 5527. doi:10.1093/mnras/staa3050

    2020 doi

  31. [40]

    2021, Mon

    de Mattia, A., Ruhlmann-Kleider, V., Raichoor, A., et al. 2021, Mon. Not. Roy. Astron. Soc., 501, 5616. doi:10.1093/mnras/staa3891

    2021 doi

  32. [41]

    2020, Mon

    Neveux, R., Burtin, E., de Mattia, A., et al. 2020, Mon. Not. Roy. Astron. Soc., 499, 210. doi:10.1093/mnras/staa2780

    2020 doi

  33. [42]

    G., Ross, A

    Hou, J., S´ anchez, A. G., Ross, A. J., et al. 2021, Mon. Not. Roy. Astron. Soc., 500, 1201. doi:10.1093/mnras/staa3234

    2021 doi

  34. [43]

    G., et al

    Blomqvist, M., du Mas des Bourboux, H., Busca, N. G., et al. 2019, Astron. Astrophys., 629, A86. doi:10.1051/0004-6361/201935641

    2019 doi

  35. [44]

    2019, Astron

    de Sainte Agathe, V., Balland, C., du Mas des Bour- boux, H., et al. 2019, Astron. Astrophys., 629, A85. doi:10.1051/0004-6361/201935638

    2019 doi

  36. [45]

    G., Aguilar, J., et al

    DESI Collaboration, Adame, A. G., Aguilar, J., et al. 2024, arXiv:2404.03000. doi:10.48550/arXiv.2404.03000

    2024 doi arXiv

  37. [46]

    G., Aguilar, J., et al

    DESI Collaboration, Adame, A. G., Aguilar, J., et al. 2024, arXiv:2404.03001. doi:10.48550/arXiv.2404.03001

    2024 doi arXiv

  38. [47]

    G., Aguilar, J., et al

    DESI Collaboration, Adame, A. G., Aguilar, J., et al. 2024, arXiv:2404.03002. doi:10.48550/arXiv.2404.03002

    2024 doi arXiv

  39. [48]

    & Loeb, A

    Jimenez, R. & Loeb, A. 2002, Astrophys. J. , 573, 37. doi:10.1086/340549

    2002 doi

  40. [49]

    2010, JCAP, 2010, 024

    Avgoustidis, A., Burrage, C., Redondo, J., et al. 2010, JCAP, 2010, 024. doi:10.1088/1475-7516/2010/10/024

    2010 doi

  41. [50]

    2015, Phys

    Liao, K., Avgoustidis, A., & Li, Z. 2015, Phys. Rev. D , 92, 123539. doi:10.1103/PhysRevD.92.123539

    2015 doi

  42. [51]

    Koksbang, S. M. 2021, Phys. Rev. Lett. , 126, 231101. doi:10.1103/PhysRevLett.126.231101

    2021 doi

  43. [52]

    2014, Re- search in Astronomy and Astrophysics, 14, 1221-1233

    Zhang, C., Zhang, H., Yuan, S., et al. 2014, Re- search in Astronomy and Astrophysics, 14, 1221-1233. doi:10.1088/1674-4527/14/10/002

    2014 doi

  44. [53]

    2010, JCAP, 2010, 008

    Stern, D., Jimenez, R., Verde, L., et al. 2010, JCAP, 2010, 008. doi:10.1088/1475-7516/2010/02/008

    2010 doi

  45. [54]

    2012, JCAP, 2012, 006

    Moresco, M., Cimatti, A., Jimenez, R., et al. 2012, JCAP, 2012, 006. doi:10.1088/1475-7516/2012/08/006

    2012 doi

  46. [55]

    2016, JCAP, 2016, 014

    Moresco, M., Pozzetti, L., Cimatti, A., et al. 2016, JCAP, 2016, 014. doi:10.1088/1475-7516/2016/05/014

    2016 doi

  47. [56]

    L., Loubser, S

    Ratsimbazafy, A. L., Loubser, S. I., Crawford, S. M., et al. 2017, Mon. Not. Roy. Astron. Soc., 467, 3239. doi:10.1093/mnras/stx301

    2017 doi

  48. [57]

    2015, Mon

    Moresco, M. 2015, Mon. Not. Roy. Astron. Soc., 450, L16. doi:10.1093/mnrasl/slv037

    2015 doi

  49. [58]

    G., & Linder, E

    Shafieloo, A., Kim, A. G., & Linder, E. V. 2012, Phys. Rev. D , 85, 123530. doi:10.1103/PhysRevD.85.123530

    2012 doi

  50. [59]

    gyu ., L’Huillier, B., Keeley, R

    Hwang, S.-. gyu ., L’Huillier, B., Keeley, R. E., et al. 2023, JCAP, 2023, 014. doi:10.1088/1475- 7516/2023/02/014

    2023 doi

  51. [60]

    E., et al

    Liao, K., Shafieloo, A., Keeley, R. E., et al. 2019, Astro- phys. J. Lett., 886, L23. doi:10.3847/2041-8213/ab5308

    2019 doi

  52. [61]

    & Liao, K

    Liu, T. & Liao, K. 2024, Mon. Not. Roy. Astron. Soc., 528, 1354. doi:10.1093/mnras/stae119

    2024 doi

  53. [62]

    E., Shafieloo, A., et al

    Li, X., Keeley, R. E., Shafieloo, A., et al. 2024, Astrophys. J. , 960, 103. doi:10.3847/1538-4357/ad0f19

    2024 doi

  54. [63]

    2020, Astrophys

    Wang, G.-J., Ma, X.-J., Li, S.-Y., et al. 2020, Astrophys. J., Suppl. Ser., 246, 13. doi:10.3847/1538-4365/ab620b

    2020 doi

  55. [64]

    2021, European Phys- ical Journal C, 81, 903

    Liu, T., Cao, S., Zhang, S., et al. 2021, European Phys- ical Journal C, 81, 903. doi:10.1140/epjc/s10052-021- 09713-5

    2021 doi

  56. [65]

    2024, Physics of the Dark Universe, 46, 101706

    Mitra, A., G´ omez-Vargas, I., & Zarikas, V. 2024, Physics of the Dark Universe, 46, 101706. doi:10.1016/j.dark.2024.101706

    2024

  57. [66]

    2024, Astrophys

    Liu, T., Cao, S., Biesiada, M., et al. 2024, Astrophys. J. Lett., 965, L11. doi:10.3847/2041-8213/ad3553

    2024 doi

  58. [67]

    & Wei, J.-J

    Ran, J.-Y. & Wei, J.-J. 2024, Phys. Rev. D , 109, 043001. doi:10.1103/PhysRevD.109.043001

    2024 doi

  59. [68]

    2023, European Physical Journal C, 83, 304

    G´ omez-Vargas, I., Medel-Esquivel, R., Garc ´ ıa-Salcedo, R., et al. 2023, European Physical Journal C, 83, 304. doi:10.1140/epjc/s10052-023-11435-9

    2023 doi

  60. [69]

    W., Lang, D., et al

    Foreman-Mackey, D., Hogg, D. W., Lang, D., et al. 2013, Publications of the Astronomical Society of the Pacific, 125, 306. doi:10.1086/670067

    2013 doi

  61. [70]

    & Clarkson, C

    Seikel, M. & Clarkson, C. 2013, arXiv:1311.6678. doi:10.48550/arXiv.1311.6678

    2013 doi arXiv

  62. [71]

    2021, Mon

    Wang, G.-J., Ma, X.-J., & Xia, J.-Q. 2021, Mon. Not. Roy. Astron. Soc., 501, 5714. doi:10.1093/mnras/staa4044

    2021 doi

  63. [72]

    & Wu, X.-F

    Wei, J.-J. & Wu, X.-F. 2017, Astrophys. J. , 838, 160. doi:10.3847/1538-4357/aa674b

    2017 doi

  64. [73]

    & Wang, F

    Yu, H. & Wang, F. Y. 2016, Astrophys. J. , 828, 85. doi:10.3847/0004-637X/828/2/85 9

    2016 doi

  65. [74]

    J., Jurek, R

    Drinkwater, M. J., Jurek, R. J., Blake, C., et al. 2010, Mon. Not. Roy. Astron. Soc., 401, 1429. doi:10.1111/j.1365-2966.2009.15754.x

    2010

  66. [75]

    & Zhang, P

    Li, Z. & Zhang, P. 2024, arXiv:2411.08498. doi:10.48550/arXiv.2411.08498

    2024 doi arXiv

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.