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CORN -- Chronometers of Relic Nature I: The first estimate of the expansion rate of the Universe using compact relic galaxies

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper reports the first cosmic-chronometer measurement of the Hubble parameter using relic galaxies, $H(z=0.15)=85.0\pm51.5\,[\mathrm{stat}]\,^{+10.2}_{-8.9}\,[\mathrm{sys}]$ km/s/Mpc, and argues that this tracer class cuts the…

desk verdict First H(z) from relic galaxies: a genuinely new tracer with honest error bars, but the SSP-only Dn4000-age calibration makes the headline systematic budget a promise rather than a demonstrated fact. read the letter →

arxiv 2608.10163 v2 pith:HPCDWUXM submitted 2026-08-10 astro-ph.CO astro-ph.GA

Krzysztof Lisiecki , Nicola Principi Cavaterra , Agnieszka Pollo , Chiara Spiniello , Laura Hunt , Charlie Rosen , Marek Biesiada , Darko Donevski
show 4 more authors
Patryk Matera Giuliano Lorenzon Katarzyna Ma{l}ek John Mills
This is my paper · ORCID
classification astro-ph.COastro-ph.GA
keywords cosmicchronometersHubbleparameterrelicgalaxiesultra-compactmassiveD_n4000indexalpha-elementenhancementstellarpopulationsynthesistension
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 paper tries to establish that relic galaxies—ultra-compact massive galaxies whose stars formed almost entirely in one short, early burst and that never merged afterward—are nearly ideal cosmic chronometers, and that using them shrinks the main astrophysical systematics of the method. As a proof of concept, it measures the expansion rate $H(z=0.15)=85.0\pm51.5\,[\mathrm{stat}]\,^{+10.2}_{-8.9}\,[\mathrm{sys}]$ km/s/Mpc from 189 relics. The result matters because the usual chronometer systematics (extended star-formation histories, mergers, metallicity) are suppressed by construction: the metallicity contribution is only about 1.2 percent, and the total systematic is 13 percent—or 8.7 percent if $\alpha$-element enhancement is ignored, as most earlier work did. The paper also identifies $\alpha$-element enhancement as the dominant remaining stellar-population systematic in metal-rich chronometers. The measurement is consistent with previous chronometer estimates and with standard cosmology within its still-large statistical uncertainty.

What carries the argument

The load-bearing object is the 4000 Å break index $D_{n}4000$ together with the calibration slope $A\equiv dD_{n}4000/dt$. The index is the ratio of continuum flux in the red bandpass 4000–4100 Å to the blue bandpass 3850–3950 Å, and it grows as a stellar population ages. The paper assumes a linear relation $D_{n}4000=A(Z,[\alpha/\mathrm{Fe}],M)\times\mathrm{age}+B$, so that the cosmic-chronometer identity $H(z)=-(1/(1+z))\,dz/dt$ becomes $H(z)=-(1/(1+z))\,A\,dz/dD_{n}4000$. The slope $A$ is measured from MILES/BaSTI single-stellar-population models as a function of metallicity and $\alpha$ enhancement; the degree-of-relicness selection is what makes it plausible to apply one SSP-calibrated $A$ to every galaxy.

What would settle it

Re-fit the same 189 relic spectra allowing composite star-formation histories (for example a few percent of young stars or a spread in metallicity) and compare the resulting $D_{n}4000$–age slope with the MILES single-burst value; if $H(z=0.15)$ shifts by more than the quoted $^{+10.2}_{-8.9}$ km/s/Mpc systematic, the single-population calibration is falsified. A complementary check is to compare this measurement with an independent, higher-precision $H(z\approx0.15)$ from another tracer.

Watch

Extended reading notes

Core claim

Using 189 ultra-compact massive galaxies selected by a high degree of relicness in $0.07\le z\le0.22$, the paper finds $\frac{dD_{n}4000}{dz}=-0.33\pm0.19\,[\mathrm{fit}]\,\pm0.07\,[\mathrm{bin}]$. Combined with the MILES single-stellar-population calibration $A\equiv \frac{dD_{n}4000}{dt}\simeq0.033$ Gyr$^{-1}$ (with $A$ depending on metallicity $Z$ and $[\alpha/\mathrm{Fe}]$), this gives the first relic-based Hubble parameter, $H(z=0.15)=85.0\pm51.5\,[\mathrm{stat}]\,^{+10.2}_{-8.9}\,[\mathrm{sys}]$ km/s/Mpc. The central discovery is not the precision of this number but the structure of its error budget: because the relic sample's metallicities sit near the turnover of the $A(Z)$ relation, metallicity contributes at most 1.2 percent, and because the sample is old and homogeneous, star-formation-history systematics are assumed subdominant. The dominant stellar-population systematic is $\alpha$-element enhancement, contributing roughly 9 percent and raising the total systematic from 8.7 to 13 percent when propagated.

Load-bearing premise

The measurement rests on treating each relic galaxy as a single stellar population: the models say how $D_{n}4000$ changes with age for one simple burst, and Section 4.3 explicitly does not test how a composite stellar population or a small admixture of younger stars would change that slope.

Editorial extensions

If this is right

  • Relic-based chronometers can reach a total systematic budget of about 13 percent with fewer than 200 galaxies, and about 8.7 percent if alpha-enhancement is treated as in earlier studies, making them competitive with the tightest current cosmic-chronometer analyses.
  • Future $D_{n}4000$ chronometer analyses should propagate $[\alpha/\mathrm{Fe}]$ explicitly; in the high-metallicity regime alpha-enhancement, not metallicity, is the leading stellar-population systematic, so fixed-$[\alpha/\mathrm{Fe}]$ analyses underestimate their errors by roughly 4 percentage points.
  • The statistical uncertainty, not the astrophysical systematics, now limits the relic-chronometer method, so the error bar should shrink roughly as the inverse square root of the number of confirmed relics as larger spectroscopic samples arrive.
  • Because the relic sample sits at the turnover of the $A(Z)$ relation, further restricting the metallicity range of a chronometer sample is a direct way to suppress the metallicity systematic toward the sub-percent level.

Reading between the lines

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

  • The paper leaves implicit that the turnover structure of $A(Z)$ is a selection principle: any chronometer tracer population whose metallicity can be measured and selected around the turnover would inherit the same suppression of the metallicity systematic, not only relics.
  • If the $[\alpha/\mathrm{Fe}]$ sensitivity found here holds up, earlier cosmic-chronometer measurements that assumed fixed $[\alpha/\mathrm{Fe}]$ may need larger error bars, with the largest shifts in the most metal-rich, high-mass galaxy samples—the samples most relevant at low redshift where the Hubble tension lives.
  • A testable extension would be to fit composite stellar populations to the same 189 relics; if the effective $D_{n}4000$–age slope moves by more than the quoted systematic when a few percent of younger stars are allowed, a composite-population correction term would be needed before relic chronometers reach their promised precision.
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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. The paper presents the first cosmic-chronometer estimate of H(z) using ultra-compact massive 'relic' galaxies. From 189 E-INSPIRE galaxies with 0.07≤z≤0.22 selected by their degree of relicness, the authors measure the redshift evolution of the D_n4000 index and calibrate the D_n4000–age slope A using MILES/BaSTI SSP models, explicitly propagating metallicity and α-element-enhancement uncertainties. They report H(z=0.15)=85.0±51.5 (stat) +10.2/−8.9 (sys) km/s/Mpc, with a systematic budget of about 13% (8.7% if [α/Fe] is not propagated), and argue that relic selection reduces SFH- and metallicity-related systematics compared with standard CC tracers. The statistical uncertainty dominates and the result is consistent with Planck and with previous CC measurements. The paper is framed as a proof of concept for relic-based chronometers.

Significance. If the result holds, the paper makes a useful proof-of-concept contribution: it introduces relic galaxies as CC tracers, explicitly quantifies the [α/Fe] contribution to the D_n4000 systematic budget, and provides several robustness tests (bin-size dependence, cosmology dependence of DoR, overlap with traditional CC selection). The paper is also transparent in stating that composite stellar populations are not modelled in the calibration. However, the headline conclusion that relic selection reduces astrophysical systematics rests on the validity of the SSP-based slope A; this is currently an untested assumption, and the composite-population issue must be addressed before the quoted systematic budget can be taken at face value. The measurement itself is honestly reported and the statistical error dominates, so the main scientific claim is modest and defensible conditional on that test.

major comments (3)
  1. [Section 4.3, Eq. (3), Fig. 5] The calibration slope A is computed from MILES SSP models only, and the text explicitly states that the impact of composite stellar populations on the D_n4000–age slope is not studied. The DoR selection does not guarantee single-burst populations: the final sample has median f_Mstar(tBB=3)=0.95±0.05, and the DoR>0.4 threshold formally allows more extended assembly histories. Because D_n4000 is a flux-weighted index, a few percent of younger stars can shift the effective slope A_eff relative to the SSP value by more than the quoted δσ_Z,α≈9%; through Eq. (4) this shifts H(z) by an amount that can exceed the quoted +10.2/−8.9 systematic uncertainty (a 20% change in A corresponds to roughly 17 km/s/Mpc). This is load-bearing for the claim of reduced astrophysical systematics. I request a quantitative test, for example using the E-INSPIRE pPXF-reconstructed SFHs to build composite-model D_n4000–age relations, or two-component models with 1–5% mass in a younger secondary component, and propagation of A_eff through Eq. (7).
  2. [Section 4.3, Section 4.4] The MILES grid has only [α/Fe]=0.0 and 0.4, and the spectra are linearly interpolated to obtain intermediate values. Because the final sample has median [α/Fe]≈0.20, both the central value A=0.033 and the α-driven systematic δσ_α≈9% depend on this interpolation, whose error is not included in the budget. The paper acknowledges the approximation, but for the claimed 'major role of α-enhancement' to be quantitatively reliable, the authors should either demonstrate that the interpolation is accurate using a different SPS grid or add an interpolation-uncertainty term to the systematic budget.
  3. [Section 4.4] The total systematic budget combines δσ_SPS=5.5%, δσ_IMF=1%, and δσ_SL=7% adopted from Moresco et al. with the relic-specific Z and [α/Fe] terms. These literature values were derived for standard passive galaxy samples and may not hold in the high-metallicity, high-[α/Fe] regime of relics; moreover, the same MILES/E-MILES model family is used both for the pPXF stellar-population parameters and for the A calibration, so the adopted 'independent' SPS/SL terms may double-count or miss shared model errors. The authors should justify the transfer of these values to relics or re-estimate at least the largest term (SL) using the actual model family and redshift range.
minor comments (5)
  1. [Abstract vs. Eq. (7)] The abstract quotes H(z=0.15)=85±53 km/s/Mpc, while Eq. (7) gives 85.0±51.5 (stat) +10.2/−8.9 (sys); please state explicitly how the total uncertainty in the abstract is formed (presumably quadrature of stat and sys).
  2. [Section 4.4 and Section 6] The total systematic uncertainty is reported as +13/−11% in Section 4.4 and as ≤12.5% in Section 6; use a consistent rounding and sign convention.
  3. [Section 4.2, Eq. (6)] Eq. (6) reports separate fit and binning uncertainties, but the text then quotes σ_stat=0.2 without stating the combination rule; please specify how these two terms are combined.
  4. [Figure 3 caption] 'restrframe' should be 'rest-frame'.
  5. [Section 2.2] The sentence 'By allowing sources with poorly constrained DoR, we are losing the most important constraint on the age' is unclear; please specify the exact effect of the σ_DoR cut on the sample, e.g., how many galaxies are removed and how the D_n4000–z slope changes when the cut is relaxed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the H(z) estimate combines an observed Dn4000-redshift slope with an independent MILES SSP calibration; no fitted parameter is renamed as a prediction.

full rationale

The derivation chain is explicit and non-circular. H(z) is computed from Eq. 4, H(z) = -1/(1+z) A dz/dDn4000, where A = dDn4000/dt is calibrated from MILES SSP models (Sec. 4.3) and dDn4000/dz = -0.33 +/- 0.19 is measured directly from the 189 relic-galaxy spectra (Eq. 6). The resulting Eq. 7 is then compared with external Planck and previous CC data, so the central value is not anchored to a benchmark. Self-citations to E-INSPIRE (Mills et al. 2025; Rosen et al. 2026) supply the sample and stellar parameters, but these are input data, not quantities derived from H(z). The acknowledged omission of composite-stellar-population effects on the Dn4000-age slope (Sec. 4.3: 'we do not study the impact of composite stellar populations on the Dn4000-age slope') is a modeling limitation that could bias the SSP calibration, but it is not a circular reduction: the paper does not fit A to the same data it then predicts. The [alpha/Fe] linear-interpolation ansatz is justified partly by self-citations, but it is a stated approximation with an explicit caveat, and its effect is propagated into the quoted systematics rather than hidden. Therefore no load-bearing step reduces to its own input; the central claim has independent observational content.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central derivation depends on the FLRW metric, a linear Dn4000-age relation, the SSP approximation for relics, a linear [alpha/Fe] interpolation, literature systematic values, and the reliability of E-INSPIRE pPXF outputs. The main free parameters are hand-chosen selection thresholds and the model-calibrated slope A. No new particles or forces are introduced.

free parameters (5)
  • DoR selection threshold = 0.4
    Chosen by hand in Section 2.2 to exclude 30% of lowest-DoR galaxies; the final sample and hence measured dDn4000/dz depend on this cut.
  • sigma_DoR threshold = 0.2
    Chosen as a compromise between robust DoR estimates and sample size; galaxy inclusion and the measured slope depend on this cut.
  • Redshift and mass selection cuts = 0.07 <= z <= 0.22, log Mstar >= 10.8
    Imposed to minimize incompleteness and volume effects; affect the sample composition and the Dn4000-z relation.
  • Dn4000-age slope A = 0.033 +0.003/-0.002
    Calibrated from MILES SSP models at the sample median Z and [alpha/Fe]; H(z) is directly proportional to A (Eq. 4), so any bias in A propagates linearly into the result.
  • Number of galaxies per redshift bin = 8
    Binning choice for the dDn4000/dz fit; authors checked robustness for bin sizes 5 to 25, so this is a minor choice but still affects the quoted slope.
assumptions (6)
  • domain assumption The FLRW metric is valid, so H(z) = -1/(1+z) dz/dt (Eq. 1).
    The cosmic chronometer method relies on this; the paper does not test it.
  • domain assumption Dn4000 depends linearly on stellar age over the relevant range (Eq. 3).
    Assumed in Section 4; the calibration fits Dn4000-age with straight lines.
  • ad hoc to paper Relic galaxies are treated as single stellar populations; composite stellar populations are not modeled in the Dn4000-age calibration.
    Section 4.3 states composite populations are not studied; the calibration A is applied to real galaxies as if each were an SSP.
  • ad hoc to paper The [alpha/Fe] dependence of MILES models is linear between [alpha/Fe]=0.0 and 0.4.
    Section 4.3 linearly interpolates the spectra; the authors note this is only an approximation.
  • domain assumption The literature systematic uncertainties SPS=5.5%, IMF<1%, SL=7% are applicable and independent of the Z/[alpha/Fe] uncertainty.
    Section 4.4 adopts these values for consistency without re-derivation; combination in quadrature assumes independence.
  • domain assumption pPXF stellar population parameters (Z, [alpha/Fe], SFH) from E-INSPIRE catalogues based on E-MILES models are accurate inputs.
    Section 2 relies on Mills et al. 2025 and Rosen et al. 2026 for DoR, Z, and [alpha/Fe]; these use the same model family as the calibration.

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Cite this review

Pith. "Pith review of CORN -- Chronometers of Relic Nature I: The first estimate of the expansion rate of the Universe using compact relic galaxies." pith.science (2026). https://pith.science/paper/HPCDWUXM

@misc{pith2026260810163,
  author       = {Pith},
  title        = {Pith review of: CORN -- Chronometers of Relic Nature I: The first estimate of the expansion rate of the Universe using compact relic galaxies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HPCDWUXM}},
  note         = {Machine review of arXiv:2608.10163}
}
read the original abstract

Measuring the expansion rate of the Universe is a central challenge in cosmology. Independent and robust methods are essential to validate existing measurements and assess potential systematic effects. We employ the cosmic chronometer (CC) approach, which uses the differential age evolution of quiescent galaxies to measure the Hubble parameter H(z) without assuming an underlying cosmological model. In contrast to previous CC studies, we restrict our analysis to relics -- ultra compact massive galaxies (UCMGs) hosting the oldest stellar populations -- thereby minimising uncertainties related to star formation history and merger history. We select a sample of 189 relic galaxies in the redshift range 0.07< z <0.22 from the E-INSPIRE UCMGs catalogue. Using the D_n4000 spectral index of relic galaxies and its redshift evolution, combined with MILES stellar population synthesis models, we derive the differential age relation required to infer H(z). We account not only for metallicity effects but also for the impact of alpha-element enhancement, which has not been explicitly propagated into the systematic uncertainty budget of the D_n4000 cosmic chronometer method. We obtain an independent measurement of H(z=0.15) = 85\pm53 km/s/Mpc. The total uncertainty is dominated by statistical limitations. The systematic component is 13% (8.7% when alpha-enrichment is not propagated), among the tightest estimates in current CC studies. We find that alpha-enrichment plays a major role in the systematic error budget, particularly in the high metallicity regime, and must be properly accounted for in future analyses. We demonstrate the proof of concept that relic galaxies provide a promising pathway to reduce systematic uncertainties in the CC method. The statistical uncertainties, which dominate the error budget, can be significantly reduced by the increase of data volume expected during the next years.

Figures

Figures reproduced from arXiv: 2608.10163 by the authors.

Figure 1
Figure 1. M⋆ as a function of redshift for E-INSPIRE galaxies, colour-coded by their DoR. The grey dashed lines show the cuts performed, and the shaded region show the cuts-limited region. Galaxies in the final sample are highlighted with a black solid contour circle. Histograms on the top- and right-side show the distribution of M⋆ and redshift covered by the galaxies. The coloured histograms encode the DoR intervals within … view at source ↗
Figure 2
Figure 2. Mass fraction assembled 3 Gyr after the Big Bang as a [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Comparison between an exemplary relic spectrum (upper, [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: Top: Dn4000 relation as a function of stellar age and colour-coded by metallicity (Z). Each point represents an SSP. Solid lines show the best linear fit for each metallicity group. Bottom: relation of slopes dDn4000/dt as a function of stellar metallicity, colour-code…
Figure 6
Figure 6. Figure 6: H(z) as a function of redshift. Empty symbols show estimates from previous CC studies, as listed at the right side of the plot (Jimenez et al. 2003; Simon et al. 2005; Stern et al. 2010; Moresco et al. 2012; Moresco 2015; Moresco et al. 2016; Zhang et al. 2014; Loubser…

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