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Gaussian Process Estimation of Transition Redshift

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Reconstructing the deceleration parameter from Hubble and supernova data puts the transition redshift at 0.59–0.68 without assuming a cosmological model.

desk verdict The SNe Ia half is built on an algebraic error in Eq. (28), producing a spurious transition redshift; the H(z) half is fine. read the letter →

arxiv 1909.00090 v1 pith:JGWGYTRU submitted 2019-08-30 astro-ph.CO gr-qc

J. F. Jesus , R. Valentim , A. A. Escobal , S. H. Pereira This is my paper · ORCID
classification astro-ph.COgr-qc PACS 98.80.-k98.80.Es95.36.+x
keywords transitionredshiftdecelerationparameterGaussianProcessH(z)dataTypeIasupernovaemodel-independentcosmologycosmicaccelerationkernelchoice
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 aims to measure the redshift at which the universe switched from deceleration to acceleration without assuming any cosmological model. It applies Gaussian Process regression, a non-parametric Bayesian technique, to 51 Hubble parameter measurements and to 1048 Type Ia supernova luminosity distances, reconstructing the deceleration parameter $q(z)$ in each case and locating its zero crossing. The H(z) data give $z_t = 0.59^{+0.12}_{-0.11}$; the supernova data, assuming spatial flatness, give $z_t = 0.683^{+0.11}_{-0.082}$. The two estimates agree and both are stable under alternative covariance kernels. These results matter because the transition redshift is a new cosmic parameter that a successful theory of cosmic acceleration must reproduce, and this is one of the few estimates that does not presuppose the theory.

What carries the argument

The engine is Gaussian Process regression, a non-parametric Bayesian method that places a distribution over functions consistent with the data and can differentiate that distribution to yield covariances for $f'$, $f''$, etc. The paper uses three covariance kernels (a squared-exponential kernel and two smoother alternatives) to test kernel dependence, and propagates uncertainties through the derived expressions for $q(z)$: $q(z) = (1+z)H'(z)/H(z) - 1$ for the Hubble data and $q(z) = (1+z)^2 D''_L(z)/(D_L(z) - (1+z)D'_L(z)) + 1$ for the supernova distances. The zero-crossing condition $q(z_t) = 0$ defines the transition redshift.

What would settle it

Generate mock $H(z)$ and Type Ia supernova catalogs from a known flat Friedmann cosmology with a known transition redshift, apply the same Gaussian Process reconstruction, and check whether the recovered $z_t$ and its quoted uncertainty contain the input value; if the derivative reconstruction is biased at low redshift, the quoted model-independent $z_t$ would be systematically off.

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Extended reading notes

Core claim

The central claim is that the transition redshift can be estimated directly from data. Reconstructing $H(z)$ and its first derivative from the 51-point H(z) compilation yields $q(z)$ through $q(z) = (1+z)H'(z)/H(z) - 1$, with a zero crossing at $z_t = 0.59^{+0.12}_{-0.11}$. Reconstructing the luminosity distance and its first two derivatives from 1048 supernovae, using $q(z) = (1+z)^2 D''_L(z)/(D_L(z) - (1+z)D'_L(z)) + 1$, gives $z_t = 0.683^{+0.11}_{-0.082}$ when spatial flatness is assumed. Both results are stable under the three covariance kernels, and the two probes agree within 1σ.

Load-bearing premise

The zero crossing of $q(z)$ is reliable only if the Gaussian Process derivative reconstructions $H'(z)$ and $D''_L(z)$ are unbiased, and the paper does not test this against simulated data; second derivatives from sparse supernova distances are especially sensitive to the kernel and the optimized length scale.

Editorial extensions

If this is right

  • The transition redshift is determined without reference to any dark-energy model, so a value near $z_t \simeq 0.6$ becomes a direct empirical target that any theory of cosmic acceleration must reproduce.
  • The agreement between the H(z) and supernova results across three covariance kernels indicates that the estimate is not sensitive to the choice of kernel.
  • The supernova-based estimate inherits the spatial-flatness assumption; within a flat universe, the two probes together constrain when cosmic acceleration began.
  • The same Gaussian Process machinery extends to reconstruct other derived functions of $H(z)$ and $D_L(z)$, such as the dark-energy equation of state, in the same model-independent way.

Reading between the lines

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

  • The quoted uncertainties are posterior errors from a single optimized kernel; systematic error from kernel choice and from the Gaussian Process prior mean is not included, so the full error budget is probably larger than reported.
  • The supernova reconstruction assumes spatial flatness. A joint Gaussian Process reconstruction of expansion and distance data could in principle relax that assumption and constrain curvature and $z_t$ simultaneously.
  • The consistency between the two probes could be sharpened with the distance-duality relation $D_L = (1+z)^2 D_A$: a future mismatch between H(z)-based and supernova-based $z_t$ would then point to new physics or systematics rather than merely different data.
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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

2 major / 5 minor

Summary. The paper uses Gaussian Process (GP) reconstructions, implemented with the GaPP package, to determine the transition redshift z_t where cosmic expansion changes from deceleration to acceleration. Two data sets are used: 51 H(z) measurements and the Pantheon SNe Ia sample. From the H(z) reconstruction, the authors obtain z_t = 0.59^{+0.12}_{-0.11}; from the SNe Ia luminosity-distance reconstruction, assuming spatial flatness, they obtain z_t = 0.683^{+0.11}_{-0.082}. These results are reported for a squared-exponential kernel and are stated to be consistent with the Matern(5/2) and Matern(7/2) kernels. The paper claims that the GP method makes the analysis model-independent, apart from the flatness assumption for the SNe Ia part.

Significance. If correct, the paper would provide useful, model-independent cross-checks of the transition redshift from two independent cosmological probes, with the strength of using the full Pantheon covariance matrix and testing three kernel choices. The H(z) result is broadly consistent with earlier estimates in the literature. However, the SNe Ia half of the central claim rests on an algebraic relation for q(z) that is incorrect, and the lack of validation of the GP derivative reconstructions leaves the quoted uncertainties unsupported. The paper is therefore not acceptable in its present form, but the issues are local and fixable by re-deriving the formula and re-running the analysis.

major comments (2)
  1. [III, Eqs. (23), (24), (28)] The derivation of q(z) from the luminosity distance is algebraically incorrect. Starting from D_L=(1+z)D_C, E=1/D_C', and q=-(1+z)D_C''/D_C'-1 (Eq. 22), the correct relation is q = 1 - (1+z)^2 D_L'' / [(1+z)D_L' - D_L]. The printed Eq. (28), q = (1+z)^2 D_L''/D_L - (1+z)D_L' + 1, has the wrong denominator and an incorrect sign; the same slip appears in Eqs. (23) and (24). For a flat LambdaCDM model at z=0.5, Eq. (28) gives q approximately +0.3 while the true deceleration parameter is approximately -0.1, so the zero crossing of Eq. (28) is not a physical deceleration-to-acceleration transition. Since Section V.B states that the q(z) reconstruction is performed "according to Eq. (28), the reported SNe Ia transition redshift in Table I is not a valid measurement as presented.
  2. [V.A and V.B] The paper asserts that Monte Carlo sampling and analytic error propagation give "negligible difference" for the q(z) uncertainties, but it does not show the comparison, and the GP derivative reconstructions are not validated against simulations. Because z_t is read off as the zero crossing of q(z), a biased GP derivative H'(z) or D_L''(z) shifts z_t systematically, and the optimized length scale and sparse high-redshift data are known to affect GP derivatives. The authors should add a mock-data test (e.g., reconstructing q(z) from a flat LambdaCDM model with the same redshift sampling) to demonstrate that the reconstructed q(z) and its zero crossing are unbiased, and they should show the Monte Carlo versus error-propagation comparison for the H(z) analysis. This is necessary to justify the quoted 1-sigma confidence intervals.
minor comments (5)
  1. [V.A] The sentence "we found negligible difference with the error propagation (29)" refers to Eq. (29), which is the SNe Ia uncertainty formula, not the H(z) uncertainty expression; the correct reference for the H(z) case is Eq. (14).
  2. [III, Eq. (27)] The Jacobian matrix in Eq. (27) is written as J = diag(sigma^2_DL), which is dimensionally inconsistent; the Jacobian should be J = diag(alpha D_Li). The final propagated variance formula is correct, but the notation should be fixed.
  3. [Table I] For the Matern(5/2) DL row, only one pair of upper/lower uncertainties is printed (0.83^{+0.25}_{-0.50}), whereas other rows list both 1-sigma and 2-sigma values; if 2-sigma values were intended, they should be provided.
  4. [Conclusion] There are small grammatical errors: "decelerator parameter" should be "deceleration parameter," and "module distance function" should be "luminosity distance function."
  5. [Throughout] Expressions such as "51 H(z) data" should read "51 H(z) data points" for clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: z_t is read off as a zero-crossing of GP-reconstructed q(z), not fitted; the SNe branch's Eq. (28) error is a correctness flaw, not a circular reduction.

full rationale

The H(z) branch is self-contained: Eq. (13), q = (1+z)H'/H - 1, is the standard kinematical definition, and z_t is not a fitted parameter but the root of the reconstructed q(z). The GP hyperparameters are optimized on the same data, but the target quantity is a feature of the reconstructed curve rather than a parameter renamed as a prediction, and the kernel dependence is explicitly tested with three kernels. The SNe branch is structurally similar: DL(z), D'_L(z) and D''_L(z) are reconstructed from Pantheon data and z_t is read off from q(zt)=0. However, Eq. (28) is not algebraically equivalent to the paper's own definitions in Eqs. (18)-(22): the correct reduction is q = 1 - (1+z)^2 D''_L / [(1+z)D'_L - D_L], while the printed Eq. (28) has a different denominator and an incorrect extra term, and the same slip appears in the unused Eqs. (23)-(24). This means the SNe z_t values are not a valid derived prediction, but this is an algebraic correctness flaw rather than a circular step: the output is not forced by construction to equal the input. No load-bearing self-citation or imported uniqueness theorem is used; Refs. [25,27] appear only for context and comparison. Therefore the circularity score is 0.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on GP hyperparameters fitted to the data, on the GP prior, on spatial flatness for the supernova analysis, and on assumptions about data independence. No new physical entities are introduced.

free parameters (3)
  • GP hyperparameters σ_f and l (Squared Exponential kernel) = not reported
    Optimized for each dataset by maximizing the log marginal likelihood, Eq. (6); they set the amplitude and correlation length and thereby control the reconstructed q(z) and z_t.
  • GP hyperparameters σ_f and l (Matern 5/2 kernel) = not reported
    Same role as for the Gaussian kernel; optimized per dataset and not reported in the paper.
  • GP hyperparameters σ_f and l (Matern 7/2 kernel) = not reported
    Same role as for the Gaussian kernel; optimized per dataset and not reported in the paper.
assumptions (5)
  • domain assumption The functions H(z), D_L(z) and their derivatives are draws from a Gaussian Process with the chosen stationary kernel.
    This is the GP prior used in Eqs. (7)-(8). If the actual data-generating functions are poorly represented by this prior, the reconstructed derivatives and z_t will be biased.
  • standard math The derivative of a Gaussian Process is also a Gaussian Process with covariance given by differentiating the kernel.
    Standard GP theory, used in Eqs. (9)-(11) to reconstruct H'(z) and D''_L(z).
  • domain assumption Spatial flatness of the FLRW metric for the SNe Ia analysis.
    Equations (16)-(19) use D_L = (1+z) D_C and E = 1/D'_C, which hold only for a spatially flat universe. The authors note this in the abstract and conclusions.
  • domain assumption SNe Ia are standardizable candles with a constant absolute magnitude after light-curve corrections, and the Pantheon covariance matrix fully characterizes the errors.
    The conversion to D_L through Eq. (25) uses a single offset M*, and the GP likelihood uses the Pantheon covariance matrix as C in Eq. (6).
  • domain assumption The 51 H(z) data points can be treated as independent with diagonal errors.
    Section IV.A describes the compilation but does not model correlations between measurements from the same survey; the GP likelihood with a diagonal C assumes independence.

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Cite this review

Pith. "Pith review of Gaussian Process Estimation of Transition Redshift." pith.science (2026). https://pith.science/paper/JGWGYTRU

@misc{pith2026190900090,
  author       = {Pith},
  title        = {Pith review of: Gaussian Process Estimation of Transition Redshift},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JGWGYTRU}},
  note         = {Machine review of arXiv:1909.00090}
}
abstract

This paper aims to put constraints on the transition redshift $z_t$, which determines the onset of cosmic acceleration, in cosmological-model independent frameworks. In order to do that, we use the non-parametric Gaussian Process method with $H(z)$ and SNe Ia data. The deceleration parameter reconstruction from $H(z)$ data yields $z_t=0.59^{+0.12}_{-0.11}$. The reconstruction from SNe Ia data assumes spatial flatness and yields $z_t=0.683^{+0.11}_{-0.082}$. These results were found with a Gaussian kernel and we show that they are consistent with two other kernel choices.

Figures

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Figure 1
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Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
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Figure 4. Figure 4: FIG. 4: Reconstruction of [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]

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Forward citations

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Reference graph

Works this paper leans on

62 extracted references · 22 canonical work pages · cited by 2 Pith papers

  1. [1]

    A. G. Riess et al. [Supernova Search Team], Astron. J. 116 (1998) 1009 [astro-ph/9805201]

    arXiv 1998

  2. [2]

    Perlmutter et al

    S. Perlmutter et al. [Supernova Cosmology Project Collaboration], Astrophys. J. 517 (1999) 565 [astro-ph/9812133]

    arXiv 1999

  3. [3]

    Astier et al

    P. Astier et al. [SNLS Collaboration], Astron. Astrophys. 447 (2006) 31 [astro-ph/0510447]

    arXiv 2006

  4. [4]

    A. G. Riess et al. , Astrophys. J. 659 (2007) 98 [astro-ph/0611572]

    arXiv 2007

  5. [5]

    T. M. Davis et al. , Astrophys. J. 666 (2007) 716 [astro-ph/0701510]

    work page Pith review arXiv 2007

  6. [6]

    Kowalski et al

    M. Kowalski et al. [Supernova Cosmology Project Collaboration], Astrophys. J. 686 (2008) 749 [arXiv:0804.4142 [astro-ph]]

    arXiv 2008

  7. [7]

    Amanullah et al

    R. Amanullah et al. , Astrophys. J. 716 (2010) 712 [arXiv:1004.1711 [astro-ph.CO]]

    arXiv 2010

  8. [8]

    Suzuki et al

    N. Suzuki et al. , Astrophys. J. 746 (2012) 85 [arXiv:1105.3470 [astro-ph.CO]]

    arXiv 2012

Show all 62 references
  1. [9]

    Komatsu et al

    E. Komatsu et al. [WMAP Collaboration], Astrophys. J. Suppl. 192 (2011) 18 [arXiv:1001.4538 [astro-ph.CO]]

    2011 arXiv

  2. [10]

    Larson et al

    D. Larson et al. , Astrophys. J. Suppl. 192 (2011) 16 [arXiv:1001.4635 [astro-ph.CO]]

    2011 arXiv

  3. [11]

    P. A. R. Ade et al. [Planck Collaboration], Astron. Astrophys. 571 (2014) A16 [arXiv:1303.5076 [astro-ph.CO]]

    2014 arXiv

  4. [12]

    D. J. Eisenstein et al. [SDSS Collaboration], Astrophys. J. 633 (2005) 560 [astro-ph/0501171]

    2005 arXiv

  5. [13]

    W. J. Percival, S. Cole, D. J. Eisenstein, R. C. Nichol, J. A. Peacock, A. C. Pope and A. S. Sza- lay, Mon. Not. Roy. Astron. Soc. 381 (2007) 1053 [arXiv:0705.3323 [astro-ph]]

    2007 arXiv

  6. [14]

    Schlegel et al

    D. Schlegel et al. [with input from the SDSS-III Collaboration], arXiv:0902.4680 [astro-ph.CO]

    arXiv

  7. [15]

    D. J. Eisenstein et al. [SDSS Collaboration], Astron. J. 142 (2011) 72 [arXiv:1101.1529 [astro- ph.IM]]

    2011 arXiv

  8. [16]

    K. S. Dawson et al. [BOSS Collaboration], Astron. J. 145 (2013) 10 [arXiv:1208.0022 [astro- ph.CO]]

    2013 arXiv

  9. [17]

    Farooq, D

    O. Farooq, D. Mania and B. Ratra, Astrophys. J. 764 (2013) 138 [arXiv:1211.4253 [astro- ph.CO]]

    2013 arXiv

  10. [18]

    Farooq and B

    O. Farooq and B. Ratra, Astrophys. J. 766 (2013) L7 [arXiv:1301.5243 [astro-ph.CO]]. 16

    2013 arXiv

  11. [19]

    Farooq, F

    O. Farooq, F. R. Madiyar, S. Crandall and B. Ratra, Astrophys. J. 835 (2017) no.1, 26 [arXiv:1607.03537 [astro-ph.CO]]

    2017 arXiv

  12. [20]

    G. S. Sharov and E. G. Vorontsova, JCAP 1410 (2014) 10, 057 [arXiv:1407.5405 [gr-qc]]

    2014 arXiv

  13. [21]

    Shapiro and M

    C. Shapiro and M. S. Turner, Astrophys. J. 649 (2006) 563 [astro-ph/0512586]

    2006 arXiv

  14. [22]

    J. V. Cunha and J. A. S. Lima, Mon. Not. Roy. Astron. Soc. 390 (2008) 210 [arXiv:0805.1261 [astro-ph]]

    2008 arXiv

  15. [23]

    A. C. C. Guimaraes, J. V. Cunha and J. A. S. Lima, JCAP 0910 (2009) 010 [arXiv:0904.3550 [astro-ph.CO]]

    2009 arXiv

  16. [24]

    N. Rani, D. Jain, S. Mahajan, A. Mukherjee and N. Pires, JCAP 1512 (2015) no.12, 045 [arXiv:1503.08543 [gr-qc]]

    2015 arXiv

  17. [25]

    J. A. S. Lima, J. F. Jesus, R. C. Santos and M. S. S. Gill, arXiv:1205.4688 [astro-ph.CO]

    arXiv

  18. [27]

    for DC(z),H(z) and q(z) parametrizations, respectively

    yieldedzt = 0.806±0.094, 0.870±0.063 and 0.973±0.058 at 1σ c.l. for DC(z),H(z) and q(z) parametrizations, respectively. It is a result compatible with our DL(z) Mat´ ern(5/2) and Mat´ ern(7/2) reconstructions. They are incompatible with all ourH(z) reconstructions 13 0.0 0.5 1...

  19. [28]

    L. Xu, W. Li and J. Lu, JCAP 0907 (2009) 031 [arXiv:0905.4552 [astro-ph.CO]]

    2009 arXiv

  20. [29]

    Jesus, R.F.L

    J.F. Jesus, R.F.L. Holanda and S.H. Pereira, JCAP 05 (2018) 073

    2018

  21. [30]

    Seikel, C

    M. Seikel, C. Clarkson and M. Smith, JCAP 06 (2012) 036

    2012

  22. [31]

    Betoule et al

    M. Betoule et al. [SDSS Collaboration], Astron. Astrophys. 568 (2014) A22 [arXiv:1401.4064 [astro-ph.CO]]

    2014 arXiv

  23. [32]

    Holsclaw et al., Phys

    T. Holsclaw et al., Phys. Rev. Lett. 105 (2010) 241302

    2010

  24. [33]

    Rasmussen and C

    C. Rasmussen and C. Williams, Gaussian Processes for Machine Learning , MIT Press, Cam- bridge U.S.A. (2006)

    2006

  25. [34]

    Shafieloo, A

    A. Shafieloo, A. G. Kim and E. V. Linder, Phys. Rev. D 85, (2012) 123530

    2012

  26. [35]

    Holsclaw et al., Phys

    T. Holsclaw et al., Phys. Rev. D 82 (2010) 103502

    2010

  27. [36]

    M. K. Yennapureddy and F. Melia, Eur. Phys. J. C (2018) 78: 258

    2018

  28. [37]

    Wei, arXiv:1808.00377 [astro-ph.CO]

    Zhao-Yu Yin and H. Wei, arXiv:1808.00377 [astro-ph.CO]

    arXiv

  29. [38]

    Melia and M

    F. Melia and M. K. Yennapureddy, JCAP 02, 034 (2018)

    2018

  30. [39]

    M. K. Yennapureddy and F. Melia, JCAP 11, 029 (2017)

    2017

  31. [40]

    A. H. Guth, Phys. Rev. D 23 (1981) 347 [Adv. Ser. Astrophys. Cosmol. 3 (1987) 139]

    1981

  32. [41]

    Melia and A

    F. Melia and A. Shevchuk, MNRAS 419 2579

  33. [42]

    Magana, M

    J. Magana, M. H. Amante, M. A. Garcia-Aspeitia and V. Motta, Mon. Not. Roy. Astron. Soc. 476 (2018) no.1, 1036 [arXiv:1706.09848 [astro-ph.CO]]

    2018 arXiv

  34. [43]

    Aghanim et al

    N. Aghanim et al. [Planck Collaboration], arXiv:1807.06209 [astro-ph.CO]. 17

    arXiv

  35. [44]

    Stern, R

    D. Stern, R. Jimenez, L. Verde, M. Kamionkowski and S. A. Stanford, Cosmic chronometers: constraining the equation of state of dark energy. I: H(z) measurements, J. of Cosmology and Astropart. Phys. 02 (2010) 008 [arXiv:0907.3149]

    2010 arXiv

  36. [45]

    Simon, L

    J. Simon, L. Verde and R. Jimenez, Constraints on the redshift dependence of the dark energy potential, Phys. Rev. D 71 (2005) 123001 [astro-ph/0412269]

    2005 arXiv

  37. [46]

    Zhang, H

    C. Zhang, H. Zhang, S. Yuan, T. J. Zhang and Y. C. Sun, Res. Astron. Astrophys. 14, no. 10, 1221 (2014) [arXiv:1207.4541 [astro-ph.CO]]

    2014 arXiv

  38. [47]

    Moresco et al., Improved constraints on the expansion rate of the Universe up to z 1.1 from the spectroscopic evolution of cosmic chronometers , J

    M. Moresco et al., Improved constraints on the expansion rate of the Universe up to z 1.1 from the spectroscopic evolution of cosmic chronometers , J. of Cosmology and Astropart. Phys. 8 (2012) 006 [arXiv:1201.3609]

    2012 arXiv

  39. [48]

    Moresco et al

    M. Moresco et al. , JCAP 1605 (2016) no.05, 014 [arXiv:1601.01701 [astro-ph.CO]]

    2016 arXiv

  40. [49]

    Moresco, Raising the bar: new constraints on the Hubble parameter with cosmic chronome- ters at z ≈ 2,, Mon

    M. Moresco, Raising the bar: new constraints on the Hubble parameter with cosmic chronome- ters at z ≈ 2,, Mon. Not. Roy. Astron. Soc. 450 (2015) L16 [arXiv:1503.01116]

    2015 arXiv

  41. [50]

    Blake et al

    C. Blake et al. , The WiggleZ Dark Energy Survey: Joint measurements of the expansion and growth history at z <1 , Mon. Not. Roy. Astron. Soc. 425(1) (2012) 405 [arXiv:1204.3674]

    2012 arXiv

  42. [51]

    Gazta˜ naga, A

    E. Gazta˜ naga, A. Cabre, L. Hui, Clustering of Luminous Red Galaxies IV: Baryon Acous- tic Peak in the Line-of-Sight Direction and a Direct Measurement of H(z), Mon. Not. Roy. Astron. Soc. 399(3) (2009) 1663 [arXiv:0807.3551]

    2009 arXiv

  43. [52]

    Anderson et al., Mon

    L. Anderson et al., Mon. Not. Roy. Astron. Soc. 439, no. 1, 83 (2014) [arXiv:1303.4666 [astro- ph.CO]]

    2014 arXiv

  44. [53]

    N. G. Busca et al. , Baryon Acoustic Oscillations in the Ly α forest of BOSS quasars , Astron. and Astrop. 552 (2013) A96 [arXiv:1211.2616]

    2013 arXiv

  45. [54]

    Delubac et al

    T. Delubac et al. [BOSS Collaboration], Astron. Astrophys. 574 (2015) A59 [arXiv:1404.1801 [astro-ph.CO]]. 18

    2015 arXiv

  46. [55]

    Font-Ribera et al

    A. Font-Ribera et al. , Quasar-Lyman α Forest Cross-Correlation from BOSS DR11: Baryon Acoustic Oscillations , J. of Cosmology and Astroparticle Phys. 05 (2014) 027 [arXiv:1311.1767]

    2014 arXiv

  47. [56]

    Oka et al., Simultaneous constraints on the growth of structure and cosmic expansion from the multipole power spectra of the SDSS DR7 LRG sample , Mon

    A. Oka et al., Simultaneous constraints on the growth of structure and cosmic expansion from the multipole power spectra of the SDSS DR7 LRG sample , Mon. Not. Roy. Astron. Soc. 439(3) (2014) 2515 [arXiv:1310.2820]

    2014 arXiv

  48. [57]

    Chuang and Y

    C.H. Chuang and Y. Wang, Modeling the Anisotropic Two-Point Galaxy Correlation Function on Small Scales and Improved Measurements of H(z), DA(z), and f(z)σ8(z) from the Sloan Digital Sky Survey DR7 Luminous Red Galaxies , Mon. Not. Roy. Astron. Soc. 435(1) (2013) 255 [arXiv:1209.0210]

    2013 arXiv

  49. [58]

    A. G. Riess, S. Casertano, W. Yuan, L. M. Macri and D. Scolnic, Astrophys. J. 876 (2019) no.1, 85 [arXiv:1903.07603 [astro-ph.CO]]

    2019 arXiv

  50. [59]

    J. L. Bernal, L. Verde and A. G. Riess, JCAP 1610 (2016) no.10, 019 [arXiv:1607.05617 [astro-ph.CO]]

    2016 arXiv

  51. [60]

    Riess, A.G. et al. , Astrophys. J. 730 (2011) 119 Erratum: [Astrophys. J. 732 (2011) 129] [arXiv:1103.2976 [astro-ph.CO]]

    2011 arXiv

  52. [61]

    find 0.33<z t < 1 at 1σ c.l., compatible with our results. 14 VI. CONCLUSION The transition from decelerated to the current accelerated phase of expansion of the universe is an important question in modern cosmology. It is well known that the transition redshift zt is strongly ...

    2017

  53. [62]

    D. M. Scolnic et al. , Astrophys. J. 859 (2018) no.2, 101 [arXiv:1710.00845 [astro-ph.CO]]

    2018 arXiv

  54. [63]

    H. Yu, B. Ratra and F. Y. Wang, Astrophys. J. 856 (2018) no.1, 3 [arXiv:1711.03437 [astro- ph.CO]]. 19

    2018 arXiv

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Reviewed August 14, 2026 · model on record in the stance chip above.