H0LiCOW V. New COSMOGRAIL time delays of HE0435-1223: $H_0$ to 3.8%
  precision from strong lensing in a flat $\Lambda$CDM model
  We present a new measurement of the Hubble Constant H0 and other cosmological
parameters based on the joint analysis of three multiply-imaged quasar systems
with measured gravitational time delays. First, we measure the time delay of
HE0435-1223 from 13-year light curves obtained as part of the COSMOGRAIL
project. Companion papers detail the modeling of the main deflectors and line
of sight effects, and how these data are combined to determine the time-delay
distance of HE 0435-1223. Crucially, the measurements are carried out blindly
with respect to cosmological parameters in order to avoid confirmation bias. We
then combine the time-delay distance of HE0435-1223 with previous measurements
from systems B1608+656 and RXJ1131-1231 to create a Time Delay Strong Lensing
probe (TDSL). In flat $\Lambda$CDM with free matter and energy density, we find
$H_0$ = 71.9 +2.4 -3.0 km/s/Mpc and $\Omega_{\Lambda}$ = 0.62 +0.24 -0.35 .
This measurement is completely independent of, and in agreement with, the local
distance ladder measurements of H0. We explore more general cosmological models
combining TDSL with other probes, illustrating its power to break degeneracies
inherent to other methods. The TDSL and Planck joint constraints are $H_0$ =
69.2 +1.4 -2.2 km/s/Mpc, $\Omega_{\Lambda}$ = 0.70 +0.01 -0.01 and $\Omega_k$ =
0.003 +0.004 -0.006 in open $\Lambda$CDM and $H_0$ = 79.0 +4.4 -4.2 km/s/Mpc,
$\Omega_{de}$ = 0.77 +0.02 -0.03 and $w$ = -1.38 +0.14 -0.16 in flat $w$CDM.
Combined with Planck and Baryon Acoustic Oscillation data, when relaxing the
constraints on the numbers of relativistic species we find $N_{eff}$ = 3.34
+0.21 -0.21 and when relaxing the total mass of neutrinos we find 0.182 eV. In
an open $w$CDM in combination with Planck and CMB lensing we find $H_0$ = 77.9
+5.0 -4.2 km/s/Mpc, $\Omega_{de}$ = 0.77 +0.03 -0.03, $\Omega_k$ = -0.003
+0.004 -0.004 and $w$ = -1.37 +0.18 -0.23.
