Cosmology-independent Estimate of the Hubble Constant and Spatial
  Curvature Using Time-delay Lenses and Quasars
  With the distance sum rule in the Friedmann-Lema\^{\i}tre-Robertson-Walker
metric, model-independent constraints on both the Hubble constant $H_0$ and
spatial curvature $\Omega_{K}$ can be obtained using strong lensing time-delay
data and Type Ia supernova (SN Ia) luminosity distances. This method is limited
by the relative low redshifts of SNe Ia, however. Here, we propose using
quasars as distance indicators, extending the coverage to encompass the
redshift range of strong lensing systems. We provide a novel and improved
method of determining $H_0$ and $\Omega_{K}$ simultaneously. By applying this
technique to the time-delay measurements of seven strong lensing systems and
the known ultraviolet versus X-ray luminosity correlation of quasars, we
constrain the possible values of both $H_0$ and $\Omega_{K}$, and find that
$H_0=75.3^{+3.0}_{-2.9}$ km $\rm s^{-1}$ $\rm Mpc^{-1}$ and
$\Omega_{K}=-0.01^{+0.18}_{-0.17}$. The measured $\Omega_{K}$ is consistent
with zero spatial curvature, indicating that there is no significant deviation
from a flat universe. If we use flatness as a prior, we infer that
$H_0=75.3^{+1.9}_{-1.9}$ km $\rm s^{-1}$ $\rm Mpc^{-1}$, representing a
precision of 2.5\%. If we further combine these data with the 1048 current
Pantheon SNe Ia, our model-independent constraints can be further improved to
$H_0=75.3^{+3.0}_{-2.9}$ km $\rm s^{-1}$ $\rm Mpc^{-1}$ and
$\Omega_{K}=0.05^{+0.16}_{-0.14}$. In every case, we find that the Hubble
constant measured with this technique is strongly consistent with the value
($\sim 74$ km $\rm s^{-1}$ $\rm Mpc^{-1}$) measured using the local distance
ladder, as opposed to the value optimized by {\it Planck}.
