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Two-rung ladder: $H_0$ from Tip of the Red Giant Branch and geometric anchors alone

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Richard Stiskalek, Harry Desmond, Guilhem Lavaux

Cosmology and Nongalactic Astrophysics · Submitted 24 Sep 2026 · 115 references

Pith's verdict: Honest, well-validated TRGB-only two-rung ladder that convincingly shows the local flow—not the TRGB calibration—sets the precision; the central H0 is model-dependent across weighting treatments, and the uncalibrated galaxy-bias model is the one soft spot I'd push on, though the negative conclusion survives regardless.

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arXiv ID2609.29996 (version 1)
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CitationGuilhem Lavaux, Harry Desmond, Richard Stiskalek. "Two-rung ladder: $H_0$ from Tip of the Red Giant Branch and geometric anchors alone." arXiv:2609.29996 (2026). https://pith.science/paper/EI77UY7I
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The paper

The paper claims

A two-rung TRGB distance ladder, built from tip-of-the-red-giant-branch magnitudes plus geometric anchors and host redshifts with no Type Ia supernova rung, cannot yet arbitrate the Hubble tension, because its precision is set by the…

The reading

This paper builds a distance ladder for the Hubble constant using only the tip of the red giant branch (the sharp bright end of the red-giant luminosity function) and two geometric anchors, the Large Magellanic Cloud and NGC 4258, dropping the Type Ia supernova rung on which the SH0ES and Carnegie-Chicago ladders both rely. It forward-models the tip magnitudes, colours, and redshifts of about 400 nearby galaxies through a reconstructed local density and peculiar-velocity field, conditioning the inference separately on each of 80 field realizations of that reconstruction. The central finding is that the precision is limited not by the TRGB calibration but by how well the local flow is known: the inferred H0 scatters by 5.2 km/s/Mpc from one field realization to the next, comparable to the SH0ES-versus-Planck difference the measurement is meant to settle. Weighting the 80 posteriors equally gives H0 = 68.4 ± 5.9 km/s/Mpc, whereas weighting by Bayesian evidence gives 72.3 ± 2.6 km/s/Mpc but collapses onto a single dominant realization, so the evidence-weighted number is fragile. The conclusion is that a TRGB-only, supernova-free ladder over the present ~1000 km/s volume cannot yet arbitrate the Hubble tension.

What carries the argument

The load-bearing elements are the hierarchical forward model of tip magnitudes, colours, and redshifts with latent host distances; the inhomogeneous-Malmquist distance prior that weights a host's possible line-of-sight positions by the reconstructed matter density through a galaxy-bias model (a sigmoid-truncated double power law in 1 + δ, Eq. 6); and the field-marginalisation step, in which the inference is run once per realization of the Manticore-Local density and velocity fields and the 80 posterior chains are combined either by their Bayesian evidence (Eq. 30) or with equal weights (Eq. 32). The split between these two weightings is what exposes that the evidence-weighted result has collapsed onto a single higher-evidence realization while the equal-weight stack carries the 5.2 km/s/Mpc field-to-field scatter.

Extended reading notes

Core claim

The paper argues that a two-rung TRGB ladder — tip magnitudes, geometric anchors, and host redshifts, with no supernova rung — is limited at the present sample depth by the reconstruction of the local density and peculiar-velocity field, not by the TRGB calibration. Across the 80 Manticore-Local realizations of the local Universe, the per-field median H0 scatters by 5.2 km/s/Mpc, and this scatter is what caps the precision. The evidence-weighted constraint H0 = 72.3 ± 2.6 km/s/Mpc is set by a single dominant realization, with an effective sample size of Neff = 1.00 out of 80, so it is sensitive to the finite sampling of the reconstruction posterior; the equal-weight stack of H0 = 68.4 ± 5.9 km/s/Mpc retains the field-to-field scatter and brackets the reconstruction sensitivity. Because at fixed realization the redshift-likelihood choice, density-smoothing scale, and sky-exposure modeling each move H0 by less than 1 km/s/Mpc, while the field-to-field scatter is 5.2 km/s/Mpc, the authors conclude that this ladder cannot yet distinguish between the competing Hubble-constant values and that the gains lie in extending the TRGB sample depth or improving the local reconstruction.

Load-bearing premise

Everything rests on the galaxy-bias model of Eq. (6), the mapping from matter overdensity to TRGB-host number density that sets the inhomogeneous-Malmquist distance prior; the authors state it has never been calibrated for their nearby low-mass host population and cite evidence that local-in-density bias models fail to reproduce halo clustering at the relevant scales.

Editorial extensions

If this is right

  • A supernova-free TRGB ladder over the present ~1000 km/s volume cannot distinguish the SH0ES and Planck values: across velocity-model variants the equal-weight H0 spans 68.4 ± 5.9 to 74.7 ± 5.2 km/s/Mpc.
  • Extending the TRGB sample beyond ~1000 km/s, where peculiar velocities are a few percent of the recession velocity, would reduce the field-to-field scatter well below the 5.2 km/s/Mpc found here.
  • Conditioning the local reconstruction on data inside the volume the hosts occupy should narrow the field-to-field spread and lift the dominant limit on this kind of ladder.
  • At fixed field realization the modelling choices that matter most are in the velocity sector: a velocity monopole shifts H0 by 5.4 ± 3.4 km/s/Mpc, whereas the redshift likelihood, density smoothing, and sky-exposure terms each move it by less than 1 km/s/Mpc.

Reading between the lines

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

  • The evidence-weighted headline of 72.3 ± 2.6 km/s/Mpc should be read as the posterior of a single field draw rather than a marginal over the reconstruction; a different or larger set of field samples would likely change which realization dominates and could swing that number materially.
  • The uncalibrated galaxy-bias model of Eq. (6) is a structurally separate fragility: even if the field-to-field scatter were reduced, an incorrect density weighting would bias the inhomogeneous-Malmquist distance prior (and hence H0) in a way the mock validation does not test, because the mocks use the same bias model for generation and recovery.
  • Because the same local density and velocity fields enter any supernova-calibrated ladder, the sensitivity documented here propagates into the SH0ES and Carnegie-Chicago calibrations; improving local reconstructions would tighten all such routes, not only this TRGB-only one.
  • Heavier-tailed redshift residuals (Student-t with ν = 2.59) indicate unresolved small-scale infall around Virgo, Fornax, and Centaurus A, so the residual scatter σv should not be read as a physical velocity dispersion; this is a direct diagnostic that the reconstructed flow is incomplete on the scales the hosts probe.
Original abstract

We infer the Hubble constant $H_0$ from the ~400 Extragalactic Distance Database hosts with a tip of the red giant branch (TRGB) distance, calibrated on the geometric anchors of the Large Magellanic Cloud and NGC 4258. We forward-model the tip magnitudes and host redshifts including magnitude-limited selection, sky exposure, and density-dependent galaxy bias, conditioning on each of the 80 Manticore-Local realisations of the local density and peculiar-velocity fields in turn. As most hosts lie at $cz_{\rm CMB} \lesssim 1000$ km/s, where peculiar velocities are important, the inference is limited by the variance of these fields rather than by the TRGB calibration. For a fixed realisation, the redshift likelihood and density smoothing each move $H_0$ by less than 1 km/s/Mpc and a velocity monopole by $5.4 \pm 3.4$ km/s/Mpc, whereas the field-to-field scatter in $H_0$ is 5.2 km/s/Mpc. Weighting the posteriors from each realisation equally gives $H_0 = 68.4 \pm 5.9$ km/s/Mpc, while weighting each by its Bayesian evidence gives $72.3 \pm 2.6$ km/s/Mpc. The latter value is set by a single particularly high-evidence realisation, making it sensitive to the finite sampling of the reconstruction posterior. This ladder therefore cannot yet arbitrate the Hubble tension. Extending the TRGB data beyond the present ~1000 km/s, together with improved reconstructions of the local Universe, would reduce the field-to-field scatter well below the 5.2 km/s/Mpc we find here.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-25: 1 request, 6,723 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.98 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.26 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We infer the Hubble constant $H_0$ from the ~400 Extragalactic Distance Database hosts with a tip of the red giant branch (TRGB) distance, calibrated on the geometric anchors of the Large Magellanic Cloud and NGC 4258. We forward-model the tip magnitudes and host redshifts including magnitude-limited selection, sky exposure, and density-dependent galaxy bias, conditioning on each of the 80 Manticore-Local realisations of the local density and peculiar-velocity fields in turn. As most hosts lie at $cz_{\rm CMB} \lesssim 1000$ km/s, where peculiar velocities are important, the inference is limited by the variance of these fields rather than by the TRGB calibration. For a fixed realisation, the redshift likelihood and density smoothing each move $H_0$ by less than 1 km/s/Mpc and a velocity monopole by $5.4 \pm 3.4$ km/s/Mpc, whereas the field-to-field scatter in $H_0$ is 5.2 km/s/Mpc. Weighting the posteriors from each realisation equally gives $H_0 = 68.4 \pm 5.9$ km/s/Mpc, while weighting each by its Bayesian evidence gives $72.3 \pm 2.6$ km/s/Mpc. The latter value is set by a single particularly high-evidence realisation, making it sensitive to the finite sampling of the reconstruction posterior. This ladder therefore cannot yet arbitrate the Hubble tension. Extending the TRGB data beyond the present ~1000 km/s, together with improved reconstructions of the local Universe, would reduce the field-to-field scatter well below the 5.2 km/s/Mpc we find here.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We infer the Hubble constant $H_0$ from the ~400 Extragalactic Distance Database hosts with a tip of the red giant branch (TRGB) distance, calibrated on the geometric anchors of the Large Magellanic Cloud and NGC 4258. contribution 0.69 0.94 0.09 asserted 1.00
s1 We forward-model the tip magnitudes and host redshifts including magnitude-limited selection, sky exposure, and density-dependent galaxy bias, conditioning on each of the 80 Manticore-Local realisations of the local density and peculiar-velocity fields in turn. method 0.99 0.93 0.02 asserted 0.99
s2 As most hosts lie at $cz_{\rm CMB} \lesssim 1000$ km/s, where peculiar velocities are important, the inference is limited by the variance of these fields rather than by the TRGB calibration. limitation 0.83 0.72 0.09 asserted 1.00
s3 For a fixed realisation, the redshift likelihood and density smoothing each move $H_0$ by less than 1 km/s/Mpc and a velocity monopole by $5.4 \pm 3.4$ km/s/Mpc, whereas the field-to-field scatter in $H_0$ is 5.2 km/s/Mpc. result 0.95 0.93 0.05 asserted 1.00
s4 Weighting the posteriors from each realisation equally gives $H_0 = 68.4 \pm 5.9$ km/s/Mpc, while weighting each by its Bayesian evidence gives $72.3 \pm 2.6$ km/s/Mpc. result 1.00 0.95 0.15 asserted 1.00
s5 The latter value is set by a single particularly high-evidence realisation, making it sensitive to the finite sampling of the reconstruction posterior. limitation 0.83 0.87 0.08 asserted 1.00
s6 This ladder therefore cannot yet arbitrate the Hubble tension. interpretation 0.75 0.66 0.81 asserted 0.96
s7 Extending the TRGB data beyond the present ~1000 km/s, together with improved reconstructions of the local Universe, would reduce the field-to-field scatter well below the 5.2 km/s/Mpc we find here. future work 1.00 0.41 0.09 hedged possibility 0.66

What kind of paper the classifier reports this is: empirical study 0.77 · evidence from analysis of existing data 0.91.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Parent EDD TRGB sample of 445 hosts with complete tabulated photometry and redshifts. (“inhomogeneous Malmquist bias”). We therefore condition the inference on Manticore-Local (McAlpine et al. 2025), a reconstruction of the local density field δ(x) and peculiar￾velocity field V (x). Manticore-Local takes as input the 2M++ galaxy com￾pilation of Lavaux & Hudson (2011). The compilation comprises 69,160 galaxies from 2MASS (Skrutskie et al. 2006) with redshifts from 2MRS (Huchra et al. 2012), 6dF￾GRS (Jones et al. 2009), and SDSS DR7 (Abazajian et al. 2009). It is Ks-limited at 11.5 in…
Figure 2. Directed acyclic graph of the hierarchical TRGB model. The global parameters and the Manticore-Local fields generate the anchor and host observables through the latent anchor distance moduli µa, the latent host distances ri, and the latent tip colours ci. The host angular coordinates (ℓi, bi) are held at their observed values by delta-function nodes, so the line-of-sight (LOS) distance is the only latent positional degree of freedom. The two plates repeat over the anchors a ∈ {LMC, NGC 4258} and the TRGB hosts. See Section 3.2 for the generative model and Section 3.3 for the…
Figure 3. Marginal H0 posteriors of the baseline Manticore-Local inference: the evidence-weighted posterior of Eq. (30) (dashed) versus the equal-weight stack of the same 80 single-field posteriors (solid, filled), against the ±1σ bands of SH0ES (Riess et al. 2022) and Planck ΛCDM (Planck Collaboration et al. 2020b). The evidence-weighted posterior peaks near 72 km s−1 Mpc−1 but has collapsed onto a single Manticore-Local realisation. ¡1610 ¡1600 ¡1590 ¡1580 log Z 60 65 70 75 80 85 H0 [km s ¡1 Mpc ¡1 ] 60 65 70 75 80 ¾v [km s ¡1 ]
Figure 4. Per-field H0 against the single-field evidence log Z for the baseline Manticore-Local model (4 h−1 Mpc density smooth￾ing, a Student-t redshift likelihood, and the 48-pixel angular sky￾exposure selection term) with error bars denoting the 1σ posterior uncertainty of each single-field run. Points are coloured by the inferred Student-t scale σv. A single realisation dominates the evidence and lies at H0 ≃ 72 km s−1 Mpc−1 , while the 80 field medians scatter by ∼5 km s−1 Mpc−1 , so the inference remains highly sensitive to the reconstruction realisation. ward model reproduces the…
Figure 5. Posterior predictive check of the angular host distribu￾tion in Galactic coordinates for the Student-t Manticore-Local model with the 48-pixel angular sky-exposure term. White cir￾cles mark the observed EDD hosts, and the coloured points the posterior-predictive sample (PPD), shaded by relative angular density. The empty band at |b| < 10◦ is the Zone-of-Avoidance mask. The exposure-weighted forward model reproduces the ob￾served host concentration across both Galactic hemispheres. gle Manticore-Local realisation weighted by the source￾density model, applies the |b| ⩾ 10◦…
Figure 6. Posterior predictive check of the TRGB tip-magnitude and CMB-frame redshift distributions for the Student-t Manticore-Local model with 4 h−1 Mpc density smoothing and the 48-pixel angular sky-exposure term, evaluated at the single dominant Manticore-Local realisation. Parameters are drawn from the posterior, and mock catalogues forward-modelled through the same selec￾tion function and inhomogeneous-Malmquist distance prior used in the inference. Top: marginal mobs and czCMB distributions of the posterior-predictive sample (PPD, blue) and the observed EDD hosts (black), each…
Figure 7. Comparison of the redshift likelihoods of the base￾line Manticore-Local run: the Gaussian (solid) and the Student-t (dashed), at their equal-weight stacked inferred scales σv = 132 and 67 km s−1 with the Student-t tail index ν = 2.59, on a loga￾rithmic density axis. The Student-t model is decisively preferred by the evidence comparison (

Figures reproduced from arXiv:2609.29996 by the authors.

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