Testing the cosmic opacity at higher redshifts: implication from quasars
  with available UV and X-ray observations
  In this paper, we present a cosmological model-independent test for the
cosmic opacity at high redshifts ($z\sim5$). We achieve this with the
opacity-dependent luminosity distances derived from nonlinear relation between
X-ray and UV emissions of quasars, combined with two types of
opacity-independent luminosity distances derived from the Hubble parameter
measurements and simulated gravitational wave (GW) events achievable with the
Einstein Telescope (ET). In the framework of two phenomenological
parameterizations adopted to describe cosmic opacity at high redshifts, our
main results show that a transparent universe is supported by the current
observational data at 2$\sigma$ confidence level. However, the derived value of
the cosmic opacity is slightly sensitive to the parametrization of $\tau(z)$,
which highlights the importance of choosing a reliable parametrization to
describe the optical depth $\tau(z)$ in the early universe. Compared with the
previous works, the combination of the quasar data and the $H(z)$/GW
observations in similar redshift ranges provides a novel way to confirm a
transparent universe ($\epsilon=0$ at higher redshifts $z\sim 5$), with an
accuracy of $\Delta \epsilon\sim 10^{-2}$. More importantly, our findings
indicate that a strong degeneracy between the cosmic opacity parameter and the
parameters characterizing the $L_{UV}-L_X$ relation of quasars, which
reinforces the necessity of proper calibration for such new type of
high-redshift standard candle (in a cosmological model-independent way).
