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The Hubble Constant determined through an inverse distance ladder including quasar time delays and Type Ia supernovae

S. Taubenberger, S. H. Suyu, E. Komatsu, I. Jee, S. Birrer, V. Bonvin, F. Courbin, C. E. Rusu, A. J. Shajib, K. C. Wong

TL;DR

The paper presents an inverse distance ladder that uses strong-lensing time-delay distances to anchor Type Ia SN distances, yielding an $H_0$ around the SH0ES value and showing only modest dependence on the cosmological background. By combining lensing with SN Ia data, the authors reduce model dependence and demonstrate a persistent tension with Planck results, underscoring a potential shortcoming of CMB-based inferences under standard models. The analysis highlights the current limitation from the small number of $D_{\Delta t}$ measurements and projects substantial gains from upcoming surveys that will tighten the $H_0$ determination and illuminate the origin of the Hubble tension. Overall, the inverse distance ladder offers a robust, model-insensitive cross-check of $H_0$ that complements local and CMB-based probes and helps guide future observational strategies.

Abstract

Context. The precise determination of the present-day expansion rate of the Universe, expressed through the Hubble constant $H_0$, is one of the most pressing challenges in modern cosmology. Assuming flat $Λ$CDM, $H_0$ inference at high redshift using cosmic-microwave-background data from Planck disagrees at the 4.4$σ$ level with measurements based on the local distance ladder made up of parallaxes, Cepheids and Type Ia supernovae (SNe Ia), often referred to as "Hubble tension". Independent, cosmological-model-insensitive ways to infer $H_0$ are of critical importance. Aims. We apply an inverse-distance-ladder approach, combining strong-lensing time-delay-distance measurements with SN Ia data. By themselves, SNe Ia are merely good relative distance indicators, but by anchoring them to strong gravitational lenses one can obtain an $H_0$ measurement that is relatively insensitive to other cosmological parameters. Methods. A cosmological parameter estimate is performed for different cosmological background models, both for strong-lensing data alone and for the combined lensing + SNe Ia data sets. Results. The cosmological-model dependence of strong-lensing $H_0$ measurements is significantly mitigated through the inverse distance ladder. In combination with SN Ia data, the inferred $H_0$ consistently lies around 73-74 km s$^{-1}$ Mpc$^{-1}$, regardless of the assumed cosmological background model. Our results agree nicely with those from the local distance ladder, but there is a >2$σ$ tension with Planck results, and a ~1.5$σ$ discrepancy with results from an inverse distance ladder including Planck, Baryon Acoustic Oscillations and SNe Ia. Future strong-lensing distance measurements will reduce the uncertainties in $H_0$ from our inverse distance ladder.

The Hubble Constant determined through an inverse distance ladder including quasar time delays and Type Ia supernovae

TL;DR

The paper presents an inverse distance ladder that uses strong-lensing time-delay distances to anchor Type Ia SN distances, yielding an around the SH0ES value and showing only modest dependence on the cosmological background. By combining lensing with SN Ia data, the authors reduce model dependence and demonstrate a persistent tension with Planck results, underscoring a potential shortcoming of CMB-based inferences under standard models. The analysis highlights the current limitation from the small number of measurements and projects substantial gains from upcoming surveys that will tighten the determination and illuminate the origin of the Hubble tension. Overall, the inverse distance ladder offers a robust, model-insensitive cross-check of that complements local and CMB-based probes and helps guide future observational strategies.

Abstract

Context. The precise determination of the present-day expansion rate of the Universe, expressed through the Hubble constant , is one of the most pressing challenges in modern cosmology. Assuming flat CDM, inference at high redshift using cosmic-microwave-background data from Planck disagrees at the 4.4 level with measurements based on the local distance ladder made up of parallaxes, Cepheids and Type Ia supernovae (SNe Ia), often referred to as "Hubble tension". Independent, cosmological-model-insensitive ways to infer are of critical importance. Aims. We apply an inverse-distance-ladder approach, combining strong-lensing time-delay-distance measurements with SN Ia data. By themselves, SNe Ia are merely good relative distance indicators, but by anchoring them to strong gravitational lenses one can obtain an measurement that is relatively insensitive to other cosmological parameters. Methods. A cosmological parameter estimate is performed for different cosmological background models, both for strong-lensing data alone and for the combined lensing + SNe Ia data sets. Results. The cosmological-model dependence of strong-lensing measurements is significantly mitigated through the inverse distance ladder. In combination with SN Ia data, the inferred consistently lies around 73-74 km s Mpc, regardless of the assumed cosmological background model. Our results agree nicely with those from the local distance ladder, but there is a >2 tension with Planck results, and a ~1.5 discrepancy with results from an inverse distance ladder including Planck, Baryon Acoustic Oscillations and SNe Ia. Future strong-lensing distance measurements will reduce the uncertainties in from our inverse distance ladder.

Paper Structure

This paper contains 5 sections, 2 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Lensing time-delay distances
  3. Inverse distance ladder: supernovae anchored with strongly lensed quasars
  4. Discussion
  5. Outlook

Figures (3)

  • Figure 1: Contour plots with 68% and 95% confidence regions for $H_0$, $\Omega_\mathrm{m}$, and $w$ in a flat $w$CDM cosmology (left-hand side), and for $H_0$, $\Omega_\mathrm{m}$, and $\Omega_\mathrm{k}$ in a non-flat $\Lambda$CDM cosmology (right-hand side). Contours based on quasar time delays and SNe Ia (JLA compilation) alone are shown in blue and green, respectively, while those using the inverse distance ladder with both probes combined are overplotted in red.
  • Figure 2: $H_0$ posteriors for different cosmologies using H0LiCOW time-delay distance measurements of four strongly lensed quasars only (left), and using the combination of the lensing measurements with the JLA SN Ia data set (right).
  • Figure 3: Comparison between the quasar time-delay + SNe Ia inverse distance ladder with other cosmological probes: CMB data from Planck (planck2018a; TT,TE,EE + lowE + lensing), a Planck + BAO + SNe Ia inverse distance ladder from aubourg2015a, and Cepheid + SN Ia data from the SH0ES project riess2019a. The mean and 68% confidence intervals for $H_0$ for different background cosmologies are shown for Planck and the two inverse distance ladders. The orange-shaded region reflects the 68% confidence interval for the SH0ES distance ladder, which is anchored locally and is thus insensitive to the cosmological background model.