# TDCOSMO IV: Hierarchical time-delay cosmography -- joint inference of the Hubble constant and galaxy density profiles

**Authors:** S. Birrer, A. J. Shajib, A. Galan, M. Millon, T. Treu, A. Agnello, M. Auger, G. C. -F. Chen, L. Christensen, T. Collett, F. Courbin, C. D. Fassnacht, L. V. E. Koopmans, P. J. Marshall, J. -W. Park, C. E. Rusu, D. Sluse, C. Spiniello, S. H. Suyu, S. Wagner-Carena  
**arXiv:** [2007.02941](https://arxiv.org/abs/2007.02941)  
**Date:** 2020-07-06  
**Summary page:** https://www.summarizepaper.com/en/paper/2007.02941v1/

## Key points

- The H0LiCOW collaboration has inferred a Hubble constant of $H_0=73.3^{+1.7}_{-1.8}$ km s$^{-1}{\rm Mpc}^{-1}$ using gravitational lensing time delays.
- Mass-sheet transform (MST) is considered to be the dominant source of residual uncertainty in this measurement.
- The team quantified MST with flexible mass models that are maximally degenerate with $H_0$.
- They applied this method to the TDCOSMO sample of 7 lenses and then added imaging and spectroscopy for 33 strong gravitational lenses from the SLACS sample.
- From their joint analysis of both samples assuming they are drawn from the same parent population, they measured $H_0=67.4^{+4.1}_{-3.2}$ km s$^{-1}{\rm Mpc}^{-1}$.
- The blind H0LiCOW, TDCOSMO-only and TDCOSMO+SLACS analyses were found to be in mutual statistical agreement.
- This study highlights the need for further research to better understand deflector mass profiles and reduce uncertainties in future measurements of Hubble Constant by physical or observational priors on the form of the mass profile, or by additional data such as spatially resolved kinematics of lens galaxies.

## Summary

The H0LiCOW collaboration has made a significant breakthrough in understanding the universe's expansion rate, as they have inferred a Hubble constant of $H_0=73.3^{+1.7}_{-1.8}$ km s$^{-1}{\rm Mpc}^{-1}$ using gravitational lensing time delays. To address the potential effect of the mass-sheet transform (MST) on this measurement - which is considered to be the dominant source of residual uncertainty - the team has quantified it with flexible mass models that are maximally degenerate with $H_0$. They applied this method to the TDCOSMO sample of 7 lenses (6 from H0LiCOW), and then added imaging and spectroscopy for 33 strong gravitational lenses from the SLACS sample and used resolved kinematics to constrain stellar anisotropy for 9 of them. From their joint analysis of both samples assuming that they are drawn from the same parent population, they measured $H_0=67.4^{+4.1}_{-3.2}$ km s$^{-1}{\rm Mpc}^{-1}$. The blind H0LiCOW, TDCOSMO-only and TDCOSMO+SLACS analyses were found to be in mutual statistical agreement. This study provides valuable insights into the universe's expansion rate and highlights the need for further research to better understand deflector mass profiles and reduce uncertainties in future measurements of Hubble Constant by physical or observational priors on the form of the mass profile, or by additional data such as spatially resolved kinematics of lens galaxies.