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

## TL;DR

This paper uses an inverse distance ladder combining strong-lensing time delays and Type Ia supernovae to measure the Hubble constant, reducing model dependence and highlighting a tension with Planck CMB results.

## Contribution

It introduces a cosmological-model-insensitive inverse distance ladder approach that combines strong-lensing and supernova data to estimate H_0.

## Key findings

- H_0 measured around 73-74 km/s/Mpc, consistent with local measurements.
- Significant tension (>2σ) with Planck CMB results.
- Future measurements will further refine the H_0 estimate.

## 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 $\Lambda$CDM, $H_0$ inference at high redshift using cosmic-microwave-background data from Planck disagrees at the 4.4$\sigma$ 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$\sigma$ tension with Planck results, and a ~1.5$\sigma$ 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.