Model-independent Constraints on Cosmic Curvature and Opacity
  In this paper, we propose to estimate the spatial curvature of the universe
and the cosmic opacity in a model-independent way with expansion rate
measurements, $H(z)$, and type Ia supernova (SNe Ia). On the one hand, using a
nonparametric smoothing method Gaussian process, we reconstruct a function
$H(z)$ from opacity-free expansion rate measurements. Then, we integrate the
$H(z)$ to obtain distance modulus $\mu_{\rm H}$, which is dependent on the
cosmic curvature. On the other hand, distances of SNe Ia can be determined by
their photometric observations and thus are opacity-dependent. In our analysis,
by confronting distance moduli $\mu_{\rm H}$ with those obtained from SNe Ia,
we achieve estimations for both the spatial curvature and the cosmic opacity
without any assumptions for the cosmological model. Here, it should be noted
that light curve fitting parameters, accounting for the distance estimation of
SNe Ia, are determined in a global fit together with the cosmic opacity and
spatial curvature to get rid of the dependence of these parameters on
cosmology. In addition, we also investigate whether the inclusion of different
priors for the present expansion rate ($H_0$: global estimation, $67.74\pm
0.46~\rm km~ s^{-1} ~Mpc^{-1}$, and local measurement, $73.24\pm 1.74~\rm km~
s^{-1} ~Mpc^{-1}$) exert influence on the reconstructed $H(z)$ and the
following estimations of the spatial curvature and cosmic opacity. Results show
that, in general, a spatially flat and transparent universe is preferred by the
observations. Moreover, it is suggested that priors for $H_0$ matter a lot.
Finally, we find that there is a strong degeneracy between the curvature and
the opacity.
