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To H0 or not to H0?

George Efstathiou

TL;DR

The paper argues that late-time modifications to the expansion history cannot resolve the Hubble tension if the early-time sound horizon $r_d$ is fixed. It introduces a dynamics-free inverse distance ladder, constrained by Pantheon SN and BAO data, showing results consistent with base $\Lambda$CDM and a Planck-derived $r_d$. It further proposes a rigorous framework that replaces an $H_0$ prior with a focus on the SN absolute magnitude $M_B$, demonstrating that any apparent phantom late-time signals arise from misinterpreting the distance ladder data. Overall, the work advocates integrating Pantheon into any forward-distance-ladder analysis and treating $M_B$ as the primary SN calibrator rather than $H_0$ itself, effectively arguing that late-time physics is unlikely to reconcile Planck and SH0ES without altering the SN calibration framework.

Abstract

This paper investigates whether changes to late time physics can resolve the `Hubble tension'. It is argued that many of the claims in the literature favouring such solutions are caused by a misunderstanding of how distance ladder measurements actually work and, in particular, by the inappropriate use of a distance ladder H0 prior. A dynamics-free inverse distance ladder shows that changes to late time physics are strongly constrained observationally and cannot resolve the discrepancy between the SH0ES data and the base LCDM cosmology inferred from Planck. We propose a statistically rigorous scheme to replace the use of H0 priors

To H0 or not to H0?

TL;DR

The paper argues that late-time modifications to the expansion history cannot resolve the Hubble tension if the early-time sound horizon is fixed. It introduces a dynamics-free inverse distance ladder, constrained by Pantheon SN and BAO data, showing results consistent with base CDM and a Planck-derived . It further proposes a rigorous framework that replaces an prior with a focus on the SN absolute magnitude , demonstrating that any apparent phantom late-time signals arise from misinterpreting the distance ladder data. Overall, the work advocates integrating Pantheon into any forward-distance-ladder analysis and treating as the primary SN calibrator rather than itself, effectively arguing that late-time physics is unlikely to reconcile Planck and SH0ES without altering the SN calibration framework.

Abstract

This paper investigates whether changes to late time physics can resolve the `Hubble tension'. It is argued that many of the claims in the literature favouring such solutions are caused by a misunderstanding of how distance ladder measurements actually work and, in particular, by the inappropriate use of a distance ladder H0 prior. A dynamics-free inverse distance ladder shows that changes to late time physics are strongly constrained observationally and cannot resolve the discrepancy between the SH0ES data and the base LCDM cosmology inferred from Planck. We propose a statistically rigorous scheme to replace the use of H0 priors

Paper Structure

This paper contains 5 sections, 19 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The Inverse Distance Ladder
  3. Should one use a SH0ES $H_0$ prior?
  4. Conclusions and Discussion
  5. Including correlations between Cepheid-calibrated SN magnitudes and magnitudes of more distant SN

Figures (5)

  • Figure 1: The evolution of the Hubble parameter with redshift. The red points show $H(z)$ measurements in three redshift bins inferred from galaxy correlations in the Baryon Oscillation Spectroscopic Survey (BOSS) Alam:2017. The purple point at $z=2.35$ shows $H(z)$ from BAO features in the cross-correlations of Ly$\alpha$ absorbers and quasars Blomqvist:2019. The blue point at $z=2.34$ shows $H(z)$ from BAO features in the correlations of Ly$\alpha$ absorbers deSainteAgathe:2019. The magenta point at $z=1.48$ shows $H(z)$ from BAO feaures in the correlations of quasars Hou:2020. The green line shows $H(z)$ for the best-fit base $\Lambda$CDM determined from Planck and the grey bands show $1\sigma$ and $2\sigma$ ranges. The dashed line shows Eq. (\ref{['equ:phantom']}) with parameters chosen to match the SH0ES value of $H_0$ at $z =0$.
  • Figure 2: 68 and 95% constraints on the parameters $\Delta$ and $z_c$ (left hand panel) and the SH0ES-like parameter $H^S_0$ of Eq. (\ref{['equ:H0Sb']}) and $H_0$. (right hand panel). The dashed lines in the right hand panel show the best fit values of $H^S_0$ and $H_0$.
  • Figure 3: The left hand panel shows 68 and 95% constraints on the parameters $H_0^S$ and $M_B$. The dotted lines show the mean values of these parameters listed in Table \ref{['tab:parameters']}. The midle panel shows the marginalised posterior distributions of the SN peak absolute magnitude $M_B$ determined from the inverse distance ladder discussed in this paper (black line) compared with the posterior distribution of $M_B$ determined from the SH0ES data (red line). The right hand panel shows the equivalent plot, but for the parameter $H^S_0$ instead of $M_B$.
  • Figure 4: The upper panel shows the magnitude-redshift relation for the Pantheon sample, together with the best fit (solid line) assuming the expansion history of Eq. (\ref{['equ:log']}). The vertical dashed line shows the maximum redshift used in the fit. The lower panel shows maximum likelihood band averaged residuals with respect to the best fit, together with $1\sigma$ errors.
  • Figure 5: 68% and 95% constraints on the NGC 4258 and LMC distance moduli for the three anchor global fit summarized in column 5 of Table \ref{['tab:fits']}. The best fit geometrical distance moduli of Reid:2019 and Pietrzynski:2019 (which are included as priors in the global fit) are shown by the dotted lines.