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