The paper delivers something real: the first Lick-index cosmic-chronometer analysis of DESI-DR1 LRGs, turning roughly 500k spectra into stacked t-z relations, a 45-point H(z) curve with full covariance over 0.36
The main problem is the one the authors themselves state in Section 6: the SPS model choice is 'likely of the same order as our combined internal systematics,' but Section 4.4's budget covers only data-management choices—S/N level, redshift-window prescriptions, quality flags. So the abstract's 'comprehensive analysis of all methodological choices' overstates the case. This matters because H(z) is extracted from the slope of age versus redshift, not from an absolute calibration; a model whose Balmer-line responses or age-metallicity behaviour is wrong in a redshift-dependent way will tilt that slope. The archaeological coherence cut also derives from the TMJ model response, so sample selection and model are coupled. The stress-test note lands on this, and the reader's conditional verdict is right. The fix is straightforward: run the stacks through at least one independent SPS model, or remove 'comprehensive' and state plainly that SPS uncertainty is not included. Without that, the quoted systematic errors are not yet believable.
Minor issues: the 355-400 km/s group is excluded with 'further details in Section C,' but Section C never provides them. And the data products (H(z) array, covariance, chains, stacks) are promised only 'in the journal version'; for a paper whose main selling point is a usable covariance matrix, that should be released at submission or, failing that, on acceptance.
The circularity burden is low and I agree with the reader that the Planck-based redshift caps only set the window, with a modest systematic spread shown when varying the prescriptions. The central cosmographic machinery holds up.
Who should read it: anyone doing model-independent H(z) tests, dark-energy reconstructions, or wanting a correlated CC dataset in 0.5
Referee Report
3 major / 5 minor
Summary. This paper applies the cosmic chronometer method to DESI-DR1 luminous red galaxies. The authors stack ~527,000 spectroscopically selected passive galaxies in velocity-dispersion and redshift bins, measure Lick indices, fit Thomas et al. (2011) stellar population models to derive ages, and build t-z relations for five velocity-dispersion groups. They then fit a pivotal-redshift cosmographic expansion around z0=0.57 to obtain H(z0)=95.1^{+10.9}_{-6.0} (stat.) ± 11.3 (syst.) km/s/Mpc, and provide a 45-point correlated H(z) sampling with a full covariance matrix. They also derive two finite-difference H(z) measurements from disjoint sets of velocity-dispersion groups, the more precise being H(z≈0.61)=88.5^{+6.7}_{-12.6} (stat.) ± 8.1 (syst.) km/s/Mpc. The paper releases stacked spectra, spectral-feature measurements, MCMC chains, and the H(z) covariance products.
Significance. If the quoted constraints are unbiased, this is a valuable addition to the cosmic-chronometer literature: it extends the method to DESI-scale samples, provides a continuously sampled H(z) band over 0.36<z<0.8, and supplies the full covariance needed for cosmological use. The velocity-dispersion corrections, the stacking methodology, and the explicit treatment of data-management systematics are careful and reproducible from the released products. The recovery of a downsizing-like age scaling relation is a useful consistency check. However, the central value and error bars rest on selection and SPS-model assumptions whose quantitative impact is not fully demonstrated; the SPS-model systematic is explicitly acknowledged in Section 6 as likely comparable to the entire internal systematic budget but is not included in the quoted errors. The paper is therefore not yet at the level of support claimed in the abstract.
major comments (3)
[Section 4.4 and Section 6] The systematic uncertainty budget is incomplete in a way that directly affects the central claim. Section 4.4 restricts the systematic budget to data-management choices (S/N level, archaeological/cosmological prescriptions, quality flags), while Section 6 states that the choice of SPS model is a known source of systematic shift and that 'existing literature suggests that this contribution is likely of the same order as our combined internal systematics.' Since the H(z) measurement is extracted from the slope of the t-z relation through Eqs. (10)-(11), a redshift-dependent SPS bias in the age estimates changes the slope and hence shifts H(z) by an amount potentially comparable to the quoted systematic errors. The abstract's phrase 'comprehensive analysis of all the methodological choices' is therefore not supported. The authors should either include a cross-SPS comparison (e.g., TMJ versus an independent model such as α-MC or Knowles et al.) or quantitatively propagate the literature estimate of SPS scatter into the systematic budget for both the cosmographic and finite-difference results.[Section 4, velocity-dispersion binning paragraph; Appendix C] The exclusion of the 355<σ[km/s]<400 velocity-dispersion group is not documented as promised. The text says 'Further details on this are given in section C,' but Appendix C discusses quality flags and the z≈0.5 oscillation and contains no analysis of the 355-400 group. This is a data-driven selection applied before the cosmographic fit: one of six velocity-dispersion groups is removed because of a reported small age offset relative to the 320-355 group. The authors should show the t-z relation for this group, quantify the offset and its origin, and demonstrate that the cosmographic results are insensitive to including or excluding it. Without this, a reader cannot assess whether the exclusion is a benign redshift-window choice or a systematic that biases the fitted slope.[Section 3, Fig. 1; Section 4.4] The 'archaeological coherence cut' couples the sample selection to the same stellar-population modeling used in the age fit. The redshift cap for each velocity-dispersion group is set by translating an age floor of 2.5 Gyr to redshift using the A25 t(σ) scaling relation and a Planck-ΛCDM z(t) prescription. The paper argues that this only limits the redshift window and does not bias the fit, and Section 4.4 does vary t(σ) and z(t) prescriptions in the systematic budget. However, all adopted t(σ) relations are empirical fits to similar data, and the cut removes exactly the low-mass, high-redshift stacks where the TMJ model response is poorest. If the scaling relation is biased, the selection is correlated with the age-redshift slope. I ask for an additional robustness test: for example, fit the t-z relations with and without the excluded low-mass high-z stacks using an independent age indicator, or show explicitly how much the fitted H(z) changes when the age floor is varied from 2.0 to 3.0 Gyr in addition to the listed t(σ) prescriptions.
minor comments (5)
[Abstract] The phrasing 'we intend apply the cosmic chronometer method' should be 'we intend to apply'.[Figure C.2 caption] The caption says 'against redshift on the left' in both clauses; the second panel is presumably on the right.[Figures 5 and 7] The legend for Jimenez et al. (2023) is labeled 'Phot.' in Fig. 5 and 'Lick' in Fig. 7; the label should be consistent.[Section 4.4] The number of alternative configurations entering the standard deviation for the systematic budget is not stated; listing the count of S/N levels, prescription combinations, and quality-flag combinations would improve transparency.[Section 5.1] The sentence describing the covariance contribution 'C_syst,ij = σ_syst(zi) σ_syst(zj)' assumes perfect correlation across all redshift bins; a brief justification of this fully correlated model would help users of the released covariance.
Circularity Check
0 steps flagged · score 0.0 of 10
No significant circularity: H(z) is derived from the slope of externally calibrated stellar ages, not from the Planck-based redshift cap.
full rationale
The derivation chain is self-contained: DESI LRG spectra are stacked in velocity-dispersion and redshift bins, Lick indices are measured, ages are fit with the TMJ stellar population model, and H(z) follows from the resulting t–z relation via either the pivotal cosmographic fit (Eqs. 8–11) or the finite-difference approximation (Eqs. 1, 14). No step fits H(z) to a quantity that already contains H(z). The only cosmological input before the fit is the 'archaeological coherence cut' (Sec. 3, Fig. 1), which uses the A25 t(σ) scaling relation and Planck-ΛCDM z(t) to impose a 2.5 Gyr age floor in redshift for each velocity-dispersion bin. The paper explicitly states that this rule 'does not provide a prior for the t−z relations' and only limits the redshift window of observation; the final H(z) values are not numerically derived from the Planck z(t) or A25 t(σ) relations. Moreover, the systematic budget varies both the t(σ) and z(t) prescriptions, finding the cut to be a minor contributor. The extensive citations to A25 are methodological (stacking, Lick-index set, priors, cosmographic framework) and do not inject A25's H(z) results into the present fit. The acknowledged omission of SPS-model variation (Sec. 6) is a robustness and accuracy limitation—it affects the quoted systematic error bars—but it is not a circularity, because the H(z) measurement does not reduce to the SPS model choice by construction. Comparisons against external literature H(z) points and the Planck-ΛCDM curve further confirm that the result is not forced by the input assumptions.
Assumptions & free parameters
9 free parameters ·
7 assumptions ·
0 invented entities
The main external inputs are the TMJ stellar population model, the DESI catalog, and the A25 scaling relations; the paper's own fitting introduces several hand-chosen thresholds (age floor, S/N, metallicity cap, quality flags) that enter the t-z data selection. No new physical entities are postulated.
free parameters (9)
H_z0 (pivotal Hubble parameter) = 95.1^{+10.9}_{-6.0} km/s/Mpc (stat), ±11.3 km/s/Mpc (syst)Amplitude parameter of the cosmographic fit that sets the H(z) scale; fitted to the t-z data.
q_z0 (deceleration parameter) = 1.0^{+2.7}_{-1.8}Second cosmographic parameter in Eq. (8), fitted with uniform prior [-10,10]; weakly constrained.
j_z0 (jerk parameter) = unconstrained; posterior matches prior, Gaussian only with priors around ±200Third cosmographic parameter; the posterior provides no information within the baseline prior.
t_z0,v (pivotal ages per velocity dispersion group) = posteriors in Fig. D.1; not tabulated numericallyOne per group, absorbed the age zero-point in Eq. (10); fitted jointly with the cosmographic parameters.
common slope m for local H(z) fits = not given explicitly; local results H(z≈0.55)=104.5 and H(z≈0.61)=88.5 km/s/MpcSlope in Eq. (14) for finite-difference measurements, with per-group intercepts t_z0,v also fitted.
Archaeological age cut = 2.5 GyrHand-chosen lower age cut to avoid TMJ low-age inaccuracy; determines redshift caps per group.
Stack S/N threshold = 150 (baseline)Hand-chosen signal-to-noise level for stacked spectra; varied from 50 to 150 to estimate systematics.
Metallicity prior cap = [Z/H] < 0.26Prior floor from A25 to keep the TMJ model in a reliable regime; alternative priors tested in Appendix B.
Quality flag thresholds = S/N(z)>50, σ_z<0.01, S/N(t)>5, σ_t<1 GyrThresholds chosen to remove low-redshift high-age stacks and unstable points; systematic tests vary them.
assumptions (7)
standard math The universe is described by an FLRW metric, so H = -1/(1+z) dz/dt is the expansion rate. The cosmic chronometer method assumes a homogeneous isotropic background; standard in cosmology.
domain assumption DESI LRGs are passively evolving galaxies that formed in short bursts and have no significant recent star formation. Required for age(z) to trace cosmic time; the sample selection aims to enforce this.
domain assumption Stacked spectra can be approximated as a simple stellar population for age and metallicity fitting. The TMJ model predicts single-burst populations, and the likelihood in Eq. (9) assumes this.
domain assumption The TMJ SPS model returns unbiased ages for t > 2.5 Gyr and [Z/H] < 0.26. The redshift caps and metallicity prior rely on this model response.
ad hoc to paper The A25 t(σ) scaling relation and a Planck-ΛCDM z(t) prescription translate age cuts into redshift windows without biasing the t-z trend. Used in Fig. 1 to define allowed redshift ranges; the paper asserts no bias but does not demonstrate independence.
domain assumption Velocity dispersion groups have parallel t-z relations, so a common slope with per-group offsets is a valid model. Assumed for the local H(z) measurements in Section 5.2.
ad hoc to paper The z≈0.5 oscillation in t-z is a systematic that can be removed with quality flags. The oscillation is excluded by the flags; the paper argues that including those points leaves posteriors unchanged.
how reviews work
Cite this review
Pith. "Pith review of Cosmography with DESI-DR1 Cosmic Chronometers: Direct H(z) measurements from Luminous Red Galaxy ages." pith.science (2026). https://pith.science/paper/2BIGKKVC
@misc{pith2026260813178,
author = {Pith},
title = {Pith review of: Cosmography with DESI-DR1 Cosmic Chronometers: Direct H(z) measurements from Luminous Red Galaxy ages},
year = {2026},
howpublished = {\url{https://pith.science/paper/2BIGKKVC}},
note = {Machine review of arXiv:2608.13178}
}
Copy review link
abstract
Providing robust redshift estimates for almost 3 million luminous red galaxies (LRGs), the Dark Energy Spectroscopic Instrument (DESI) offers a unique opportunity to test the expansion rate of the Universe with independent approaches. We apply the cosmic chronometer method to derive new, independent constraints on the Hubble parameter at 0.3<z<1.2 from the differential age evolution of DESI LRGs. We select spectra applying spectroscopic cuts to ensure sample purity and remove contamination by star-forming objects, then build a robust sample of cosmic chronometers (CCs) by stacking to obtain stable, high signal-to-noise (S/N) spectra, which also serves as a democratic binning choice for the $t-z$ plane. Ages are estimated by measuring Lick indices on the stacked spectra and fitting them with a theoretical stellar population model. We obtain $t-z$ relations from which we derive $H(z)$ constraints via two independent approaches: a fit with a pivotal-redshift cosmography, and a direct estimate from the original CC method. The cosmographic fit yields posteriors for the kinematic parameters $\{H_{z_0}, q_{z_0}, j_{z_0}\}$ compatible with currently considered cosmologies, giving a precision-level estimate of $H(z)$. We provide the maximum-a-posteriori (MAP) $H(z)$ estimate, an array of the median confidence region in the $H-z$ plane, and its covariance matrix. We also leverage the redshift distributions of the $t-z$ relation for different velocity dispersion groups to obtain two independent local measurements using the discrete approximation $H(z) \approx -\Delta z/[\Delta t (1+z)]$; the one from the reddest envelope of CCs gives $H(z \approx 0.61) = 88.5^{+6.7}_{-12.6}$ (stat.) $\pm 8.1$ (syst.) km s$^{-1}$ Mpc$^{-1}$. Systematic uncertainties for both the cosmographic and discrete $H(z)$ measurements come from a comprehensive analysis of all methodological choices in the data treatment.
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Reviewed August 15, 2026 · model on record in the stance chip above.