Cosmography with DESI-DR1 Cosmic Chronometers: Direct H(z) measurements from Luminous Red Galaxy ages

This paper presents a new, model-independent estimate of the expansion history of the Universe using the cosmic chronometer (CC) approach applied to early-type galaxies (ETGs). The authors employed the recently released spectra from the DESI-DR1 survey, specifically targeting Luminous Red Galaxies (LRGs). The vast scale of the survey provided over 2 million usable LRG spectra, from which they selected a spectroscopically refined subsample of 527,287 sources. These spectra were distributed into logarithmically spaced velocity dispersion groups and stacked by increasing redshift, refining the methodology introduced in A25. This procedure yielded highly stable stacked spectra with a median signal-to-noise ratio, ⟨S/N⟩, of ≈ 150, with deviations of less than 1%. The authors emphasize the importance of applying a sensible redshift cut for each velocity dispersion group to avoid the inclusion of young stellar populations, an age regime where the stellar population synthesis (SPS) model used here, Thomas et al. (2011) (TMJ), may not respond with sufficient accuracy.

As part of the analysis, the authors measured the 25 standard Lick indices plus 8 additional spectral features: [OII]3726/3729 (treated as a doublet due to resolution limits), CaII K, CaII H, D4000, Dn 4000, Hβ0, [OIII]5007, and Hα. These measurements, performed using the specialized pyLick code (Borghi et al. 2022) on the full parent sample, are provided as supplementary material. The individual and stacked spectra are also made available upon request, alongside a compact summary of the metadata and line index measurements for the stacks.

For the central cosmographic analysis, the authors implemented a pivotal cosmographic framework, as recently explored by Fazzari et al. (2025), which allows for a Taylor expansion of the Hubble parameter around a non-zero pivotal redshift, z0. This provides a more flexible alternative to traditional expansions around z = 0. Through this approach, they obtained a Hubble parameter estimate at z0 ≈ 0.57 of H = 95.1+10.9−6.0 (stat.) ± 11.3 (syst.) km s−1 Mpc−1. The systematic uncertainty budget accounts for all methodological choices made after the spectrophotometric selection, including the ⟨S/N⟩ threshold for stacking, the archaeological coherence cut, and the quality flags applied to the t − z plane. The uncertainty from velocity dispersion corrections is integrated into the statistical error by construction. While the choice of SPS model is a known source of systematic shift (e.g. Moresco et al. 2020), exploring multiple models exceeded the scope of this work; however, existing literature suggests that this contribution is likely of the same order as the combined internal systematics.

The primary strength of this cosmographic approach lies not in a single local measurement, but in the reconstructed expansion history across the redshift range. The authors provide a set of median H(z) values sampled in steps of ∆z = 0.01 from z = 0.36 to z = 0.80, representing the limits of the data. Alternatively, the expansion can be described using the third-order functional approximation of H with the modal values for the cosmographic parameters Hz0, qz0, jz0. These measurements are, by construction, not independent, and therefore the full covariance matrix, which incorporates systematic contributions, is included. To facilitate further statistical studies, the full MCMC chains for the baseline cosmographic fit are also provided.

Finally, to allow for comparison with the broader CC literature, the authors provide two statistically significant local measurements derived using the finite difference approximation, H(z0) ≈ −∆z/((1 + z0)∆t), on separate velocity dispersion groups. They estimate H(z ≈ 0.55) = 104.5+13.2−7.6 (stat.) ± 22.4 (syst.) km s−1 Mpc−1 and H(z ≈ 0.61) = 88.5+6.7−12.6 (stat.) ± 8.1 (syst.) km s−1 Mpc−1. Both measurements come from slightly physically different CCs (massive and supermassive ETGs) and thereby should not be considered as a redshift evolution of the exact same observable. Moreover, the latter measurement should be regarded as the most stringent, as it comes from the reddest envelope of passively evolving ETGs, which according to the CC framework, constitutes the purest sample. Regarding systematic effects, for these local estimates, a third component was included to account for potential departures from linearity (finite difference approximation), coming from the redshift bins being slightly broader than some of those used in the literature. These measurements represent a highly independent and statistically robust contribution to the current observational constraints on the expansion of the Universe.

Improvements to AI Systems Based on This Paper:

1. AI-Driven Spectroscopic Stacking Optimizer

• Improvement: Train an AI model to automatically determine optimal redshift cuts per velocity dispersion group, using the paper’s finding that avoiding young stellar populations is critical for SPS accuracy.

• Capability: The AI can predict the maximum redshift for each stellar population group to maximize signal-to-noise while minimizing age-induced systematic errors, producing more reliable stacked spectra for any galaxy survey.

2. Uncertainty-Aware Cosmographic Parameter Estimator

• Improvement: Implement a neural network that directly learns the mapping from stacked spectral indices (e.g., Lick indices, D4000, Hβ) to cosmographic parameters (H, q, j) with full covariance propagation, incorporating the paper’s pivotal redshift expansion around z0 ≠ 0.

• Capability: The AI can provide real-time, model-independent H(z) reconstructions with statistically rigorous error bars, including systematic contributions from SPS model choice, stacking thresholds, and quality flags—without requiring manual MCMC chains.

3. Automated Systematic Budget Auditor

• Improvement: Build an AI system that automatically identifies and quantifies all methodological systematic contributions (e.g., S/N threshold, coherence cuts, t–z plane flags) by simulating perturbations to the pipeline, as done manually in this paper.

• Capability: The AI can audit any new cosmic chronometer dataset and output a breakdown of statistical vs. systematic uncertainties, flagging dominant error sources and suggesting optimal parameter choices for future surveys.

4. Redshift-Dependent Stellar Population Classifier

• Improvement: Use the paper’s refined subsample of 527,287 LRGs to train a classifier that distinguishes passively evolving ETGs from those with young stellar populations, based on spectral features like [OII] and Hβ0.

• Capability: The AI can automatically filter large spectroscopic surveys (e.g., DESI, Euclid) to select only the purest cosmic chronometer candidates, improving the accuracy of H(z) measurements at higher redshifts.

5. Covariance-Aware Interpolation Network for H(z)

• Improvement: Develop a generative model (e.g., normalizing flow) trained on the paper’s MCMC chains and covariance matrices to produce smooth, non-parametric H(z) functions with correlated uncertainties across z = 0.36–0.80.

• Capability: The AI can generate arbitrary H(z) samples for cosmological model fitting, enabling faster and more accurate constraints on dark energy and modified gravity theories without re-running expensive MCMC.

6. Cross-Survey Systematic Transfer Learner

• Improvement: Leverage the paper’s comparison of local H(z) measurements from different velocity dispersion groups to train a transfer learning model that corrects for systematic offsets between different cosmic chronometer samples (e.g., massive vs. supermassive ETGs).

• Capability: The AI can harmonize H(z) data from multiple surveys (e.g., DESI, SDSS, VLT) into a single consistent dataset, reducing tension in cosmological parameter estimates and improving the robustness of expansion history reconstructions.

7. Real-Time Spectral Index Prediction from Raw Spectra

• Improvement: Train a deep learning model to predict the 33 measured spectral indices (25 Lick + 8 additional) directly from raw galaxy spectra, mimicking the pyLick code but with faster inference.

• Capability: The AI can process millions of spectra in minutes, enabling rapid generation of cosmic chronometer datasets for transient events or large-area surveys, with uncertainty estimates derived from the paper’s stacking stability (<1% deviations).