# The Hubble-Lema\^{i}tre constant and sound horizon from low-redshift probes

## TL;DR

This paper investigates the tension between CMB and low-redshift measurements of the Hubble constant, using independent distance calibrations to estimate the sound horizon scale and H0 without assuming a specific cosmological model.

## Contribution

It provides a model-independent estimate of H0 and r_s by combining lensing, supernovae, and BAO data, challenging the CMB-inferred values.

## Key findings

- H0r_s = (9895 ± 161) km/s
- H0 = (72 ± 7) km/s/Mpc
- r_s = (137 ± 4.5) Mpc, lower than CMB estimates

## Abstract

We revisit the claimed tension, or lack thereof, of measured values of the Hubble-Lema\^{i}tre parameter $H_0$ from Cosmic Microwave Background (CMB) data and low-redshift indicators. Baryon Acoustic Oscillations (BAO) rely on the scale of the sound horizon at recombination $r_s$ to convert angular measurements into angular-diameter distances, so fixing $r_s$ from CMB measurements already constrains $H_0.$ If departures from concordance cosmology are to be constrained, truly independent measurements of $H_0$ are needed. We use the angular-diameter distances to three time-delay lenses from the H0LiCOW collaboration to calibrate the distance ladder, combine them with relative distances from Supernovae Ia and BAO, leaving $r_s$ completely free, and provide the inferred coefficients ($q_{0},j_{0},s_{0}$) in the polynomial expansion of H(z). We obtain $H_{0}r_{s}=(9895\pm161)$km/s and $H_0=(72\pm7)$km/s/Mpc. Combined with $H_0$ from H0LiCOW, then $r_s=(137\pm4.5)$Mpc is consistent with previous work and systematically lower than the CMB-inferred value. Our results are independent of the adopted cosmology, and removing Supernovae with z<0.1 has a negligible effect.