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Supernovae Ia, high-redshift probes, and the Hubble tension: current status and future perspectives

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A binned analysis of the Pantheon and Pantheon+ supernova samples reports a mild decrease of the Hubble constant with redshift, parametrized as H0(z) = H0'/(1+z)^eta with eta ~ 0.01.

desk verdict A clear proceedings summary of the authors' own binned H0 work, overstating a trend that remains sensitive to the fixed-M assumption; not a new contribution but acceptable as a status report after minor revision. read the letter →

arxiv 2501.14944 v1 pith:SKCLCTJC submitted 2025-01-24 astro-ph.CO

Maria Giovanna Dainotti , Biagio De Simone This is my paper · ORCID
classification astro-ph.CO
keywords HubbletensionsupernovaeIabinnedanalysisredshiftevolutionH0(z)gamma-rayburstsquasarsstandardcandles
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 review paper reports the authors' earlier finding that when type Ia supernovae from the Pantheon and Pantheon+ catalogs are split into redshift-ordered bins and the Hubble constant is estimated separately in each bin, H0 decreases with redshift according to H0(z)=H0'/(1+z)^eta with eta ~ 0.01. The authors present this as evidence either for hidden astrophysical evolution of supernova parameters with redshift, such as the known stretch evolution, or for cosmological models beyond flat Lambda CDM, including f(R) modified gravity and scale-invariant SCDM. The paper also surveys gamma-ray bursts and quasars as high-redshift standard candles whose correlations can extend the Hubble diagram from z~2.3 out to z~10, providing a path to test whether the decline continues. A sympathetic reader should care because a redshift-dependent H0 would change how the Hubble tension is framed and how distance-ladder calibrations are done.

What carries the argument

The load-bearing machinery is the binned H0(z) analysis: the supernova catalog is ordered in redshift and cut into equipopulated bins (3, 4, 20, or 40); in each bin, a Markov Chain Monte Carlo fit to the distance moduli estimates H0 while other parameters are held fixed or allowed to vary, using the chi-square likelihood with the full covariance matrix. The absolute magnitude M is recalibrated so the lowest-redshift bin returns H0 = 73.5 km/s/Mpc (or a default M is kept), and the resulting per-bin H0 values are fitted with the power-law H0(z)=H0'/(1+z)^eta, whose exponent eta is the evolutionary diagnostic. For extending to high redshift, the paper relies on the Dainotti 3D (fundamental plane) correlation for gamma-ray burst afterglows and the Risaliti–Lusso relation for quasar X-ray versus UV luminosity, both used to standardize candles beyond the SNe Ia range.

What would settle it

Run the same binned MCMC pipeline on simulated Pantheon-like catalogs generated with a single true H0 and no redshift evolution; if the procedure recovers eta significantly different from zero, the trend is an artifact. Alternatively, a model-independent, binned estimate of H0 from the same data—using nonparametric distance reconstruction without assuming the power-law form—that yields eta consistent with zero would disprove the claimed evolution.

Watch

Extended reading notes

Core claim

The central claim is that the Hubble constant inferred from SNe Ia is not constant when the sample is divided by redshift: in the Pantheon sample, MCMC fits to 3, 4, 20, and 40 equipopulated bins yield a decreasing H0(z) with evolutionary coefficient eta ~ 0.01 in the functional form H0(z)=H0'/(1+z)^eta. Under LambdaCDM and w0waCDM, eta is compatible with zero at 1.2–2.0 $\sigma$ when H0 is the only free parameter, and up to 5.8 $\sigma$ when the parameter space is expanded to include Omega_M or w_a together with BAO constraints. For the SCDM cosmology, eta ~ 0.01 persists for both Pantheon and Pantheon+, with compatibility with zero at 5.3–13.6 $\sigma$ and 4.8–9.7 $\sigma$, respectively. The authors conclude that the data either hide a redshift evolution of SNe Ia properties or point to a cosmology beyond the standard model.

Load-bearing premise

The result stands on the assumption that the per-bin H0 estimates are unbiased, so the fitted decline is not an artifact of the absolute-magnitude recalibration, the number or composition of the bins, the covariance matrix, or the imposed power-law form.

Editorial extensions

If this is right

  • If the trend is real, the Hubble tension is not merely a mismatch between two numbers but a function of redshift, and future single-number H0 comparisons should be replaced by H0(z) comparisons.
  • SNe Ia standardization parameters, in particular the stretch distribution, would need to evolve with redshift, affecting distance-ladder calibrations at z > 0.1.
  • The result would favour alternative cosmologies such as f(R) modified gravity or scale-invariant SCDM over flat Lambda CDM, provided systematic biases are excluded.
  • Extending the same binned analysis to GRB and quasar samples would move the test of H0 evolution to z ~ 2–10, where SNe Ia are absent.
  • Upcoming high-z SNe Ia from JWST, Roman, and Subaru can directly measure the trend and discriminate between astrophysical evolution and new cosmology.

Reading between the lines

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

  • The reported eta could be an artifact of the choice to calibrate M against the first bin; a simulation study with a null input H0 would reveal whether the procedure itself generates a spurious decline.
  • The functional form H0(z)=H0'/(1+z)^eta imposes a monotonic decline; a more flexible fit might uncover a plateau or a transition redshift, which would carry different physical implications.
  • The significance jump from 1.2–2.0 sigma (one free parameter) to 5.8 sigma (two free parameters with BAOs) suggests the trend's strength depends heavily on the assumed model space, so the robustness of eta across different likelihoods is a key test.
  • The quasar golden sample reaching Omega_M precision comparable to SNe Ia makes it feasible to bin quasars by redshift and search for the same H0(z) trend independently, a cross-check the paper mentions but does not perform.
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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 / 4 minor

Summary. This proceedings contribution by Dainotti and De Simone summarizes the authors' binned analyses of the Pantheon and Pantheon+ SNe Ia samples, which claim a decreasing Hubble constant with redshift described by H0(z)=H0'/(1+z)^η with η≈0.01 (Eq. 2). The paper discusses whether this trend indicates redshift evolution of SNe Ia parameters or new cosmology, and it reviews Gamma-Ray Bursts (GRBs) and quasars (QSOs) as high-redshift probes. No new analysis is presented; the central numbers are quoted from the authors' earlier papers [24-26], and the figures are reproduced from those works.

Significance. If the claimed η≈0.01 trend is genuine, it would have direct implications for the Hubble tension, either pointing to hidden evolution of SNe Ia properties or to a breakdown of flat ΛCDM. The paper is useful as a compact review of the authors' methodology and of current high-z probe efforts, and it honestly mentions the astrophysical-evolution alternative in Section 2. However, the manuscript does not include the actual binned data, fitted values, or goodness-of-fit statistics, and the reported η is obtained while fixing the SNe Ia absolute magnitude M; the central claim therefore inherits all of its support from the authors' earlier papers and is not self-contained. The paper also contains inconsistent significance statements across Sections 2 and 3. No machine-checked proofs or independent verification are provided.

major comments (3)
  1. [Section 2, Eq. (2)] The manuscript reports η≈0.01 but never lists the fitted values of H0' and η, their uncertainties, the per-bin H0 estimates, or the goodness of fit (e.g., χ²/dof) for any of the 3, 4, 20, or 40 bin configurations or for the ΛCDM and w0waCDM models. Without these numbers, the reader cannot assess whether Eq. (2) actually describes the binned data or whether the quoted significance is meaningful. Please add a table with the per-bin H0 values and errors, the best-fit η with its 1σ uncertainty, and the goodness of fit for each configuration.
  2. [Sections 2 and 3] The significance of the η measurement is stated inconsistently: Section 2 says η is compatible with zero at 1.2-2.0σ, Section 3 says 'compatibility with zero is reached up to 5.8σ', and then quotes 'compatibility with zero' of 5.3-13.6σ for Pantheon and 4.8-9.7σ for Pantheon+ from [26]. These statements cannot all describe the same single η≈0.01 unless they refer to different models, bin counts, and treatments of M, but the paper does not specify the correspondence. The phrase 'compatibility with zero' is also ambiguous; it should be replaced with 'significance of the deviation from zero.' Please provide a table that lists, for each result, the sample, model, number of bins, treatment of M, and the reported η with its significance.
  3. [Section 2] The binned analysis fixes the SNe Ia absolute magnitude M by recalibrating to H0=73.5 km/s/Mpc in the first bin and then fits H0 as the only free parameter in each bin. Because the distance modulus depends on H0 and M through their difference (μ = 5 log10(d_L) − 5 log10(H0) + ...), any redshift evolution of M—such as the stretch evolution cited from [32]—will be absorbed into the fitted H0(z). The manuscript mentions this possibility qualitatively but does not test whether the trend persists when M is allowed to vary. To make the central claim load-bearing, the authors should either fit M as a free parameter (e.g., M(z)=M0+αz) and report how η changes, or explicitly reframe the abstract and conclusions as describing a degeneracy between H0(z) and M(z).
minor comments (4)
  1. [Section 1] The sentence ending '...has been applied GRBs and QSOs represent together a future perspective on the high-z cosmology' is grammatically incomplete and should be rewritten.
  2. [Section 5] The sentence 'The test of further SNe Ia samples in undergoing [39]' is ungrammatical; it should be revised, and the reference [39] should be clearly marked as a submitted paper.
  3. [Section 3] The phrase 'with a compatibility with zero that ranges from 5.3σ to 13.6σ' is ambiguous and should be rephrased as the 'significance of the deviation from zero' to avoid confusion about the direction of the effect.
  4. [Figures 1 and 2] The captions state that the figures are reproduced from [24] and [25]; if the journal requires permission for reproduced figures, please confirm that this has been obtained.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the reported η≈0.01 is a fitted parameter from the authors' earlier binned SNe Ia analyses, not a prediction forced by definition, and the fixed-M caveat is a data-interpretation degeneracy explicitly acknowledged in the text.

full rationale

This paper is a proceedings summary rather than a new derivation. In Sections 2 and 3, the derivation chain is: chi-square likelihood (Eq. 1) -> per-bin MCMC estimates of H0 -> fit to H0(z)=H0'/(1+z)^eta (Eq. 2). The text states, "After the values of H0 are found, a fitting with a decreasing function of the redshift is conducted," so eta is explicitly a fit output and not a prediction. Nothing in Eq. 2 or the likelihood defines H0(z) in terms of eta by construction; a flat trend (eta=0) is allowed by the fit, and the reported compatibility with zero shows the result is data-dependent rather than forced. The fixed-SNe-Ia-absolute-magnitude caveat raised in the skeptic summary is a physical degeneracy between M and H0, not a logical circularity; the paper itself acknowledges it: "This decreasing trend for H0 with redshift can be explained in light of possible astrophysical biases or redshift-drift for SNe Ia parameters, like what is observed with the stretch, see [32]." The reliance on [24-26] is self-citation, but those are peer-reviewed, externally falsifiable analyses of public Pantheon/Pantheon+ data, and no uniqueness theorem or definitional equivalence is imported from them. Therefore no circular step can be exhibited.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper's central claim rests on fitted parameters from Eq. (2), a calibration of the SNe Ia absolute magnitude, the assumed cosmological models, and the adopted GRB/QSO correlations. No new entities are introduced.

free parameters (4)
  • H'_0 (amplitude of H0 at z=0)
    Free parameter in Eq. (2), fitted to the binned H0 values; the numerical value is not reported in this review.
  • eta (evolutionary coefficient) = ~0.01
    Fitted slope in Eq. (2); the paper's central summarized result.
  • SNe Ia absolute magnitude M (recalibration) = chosen so first bin yields H0 = 73.5 km/s/Mpc
    Section 2 recalibrates M to anchor the first bin; this choice can influence the apparent trend.
  • Omega_M or w_a (background model parameters)
    In Section 3 these are free-to-vary alongside H0 in the MCMC; values are not reported.
assumptions (5)
  • domain assumption The covariance matrix C in Eq. (1) correctly captures statistical and systematic uncertainties of the Pantheon sample.
    Section 2 builds the chi-square likelihood on this matrix; if it is wrong, the per-bin H0 values and the trend are not reliable.
  • domain assumption Anchoring the first redshift bin to H0 = 73.5 km/s/Mpc via recalibration of M does not bias the higher-redshift bins.
    Section 2 recalibrates M so the first bin gives H0=73.5; the trend claim assumes this anchoring is neutral.
  • ad hoc to paper The functional form H0(z)=H0'/(1+z)^eta is a valid description of any real redshift evolution.
    Equation (2) is assumed without derivation; a different monotonic form would give a different eta.
  • domain assumption Lambda CDM and w0waCDM provide the correct distance modulus-redshift relation for the bins.
    Section 2 computes mu_th within these two models; the resulting H0 values depend on this choice.
  • domain assumption The GRB Dainotti 3D relation and the QSO Risaliti-Lusso relation are valid standardizable correlations after correction for selection effects.
    Section 4 relies on these correlations to treat GRBs and QSOs as cosmological probes; the correlations are taken from the cited literature.

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Cite this review

Pith. "Pith review of Supernovae Ia, high-redshift probes, and the Hubble tension: current status and future perspectives." pith.science (2026). https://pith.science/paper/SKCLCTJC

@misc{pith2026250114944,
  author       = {Pith},
  title        = {Pith review of: Supernovae Ia, high-redshift probes, and the Hubble tension: current status and future perspectives},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SKCLCTJC}},
  note         = {Machine review of arXiv:2501.14944}
}
abstract

The Hubble constant ($H_0$) tension is one of the biggest challenges in modern cosmology. This consists of the discrepancy, at around $5\sigma$, between the local value of $H_0$ measured through Supernovae Ia (SNe Ia) constrained with the Cepheids and the value inferred from the observations of Cosmic Microwave Background (CMB) by Planck data. According to the most appealing cosmological models, such as the flat $\Lambda$CDM, the $H_0$ should not vary according to the measurement method or the redshift $z$ of the probe used for estimating it. Thus, many ideas have been proposed in the literature to face this tension. In the current work, we summarize the results obtained with the binned analysis of SNe Ia, showing a decreasing trend for $H_0$ with $z$ with an evolutionary coefficient $\eta \sim 0.01$, and we further discuss the impact of high-$z$ probes such as Gamma-ray Bursts (GRBs) and quasars (QSOs) that allow reaching constraints on the cosmological parameters that will extend the Hubble diagram to high-$z$ values.

Figures

Figures reproduced from arXiv: 2501.14944 by the authors.

Figure 1
Figure 1. The 𝐻0 (𝑧) fitting in the case of 3 and 4 bins extracted from the Pantheon sample. Upper left panel. 3 bins within ΛCDM. Upper right panel. 3 bins within 𝑤0𝑤𝑎CDM. Lower left panel. 4 bins within ΛCDM. Lower right panel. 4 bins within 𝑤0𝑤𝑎CDM. This Figure is reproduced from [24]. The results in [24] show that a mild evolution of 𝐻0 with 𝑧 is present. The 𝜂 is ∼ 0.01 and is compatible with zero in the range from 1.2𝜎 … view at source ↗
Figure 2
Figure 2. The 3 bins fitting of 𝐻0 (𝑧) in the case of Pantheon with two free parameters. Left panel. 3 bins within ΛCDM. Right panel. 3 bins within 𝑤0𝑤𝑎CDM. This Figure is reproduced from [25]. choosing the default 𝑀 = −19.35 value for Pantheon that corresponds to 𝐻0 = 70 𝑘𝑚 𝑠−1 𝑀 𝑝𝑐−1 in the first bin out of 3. After performing the same analysis discussed in Section 2, the results show 𝜂 ∼ 0.01, and its compatibility with ze… view at source ↗

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.