Assessment of the cosmic distance duality relation using Gaussian
  Process
  Two types of distance measurement are important in cosmological observations,
the angular diameter distance $d_A$ and the luminosity distance $d_L$. In the
present work, we carried out an assessment of the theoretical relation between
these two distance measurements, namely the cosmic distance duality relation,
from type Ia supernovae (SN-Ia) data, the Cosmic Chronometer (CC) Hubble
parameter data, and baryon acoustic oscillation (BAO) data using Gaussian
Process. The luminosity distance curve and the angular diameter distance curve
are extracted from the SN-Ia data and the combination of BAO and CC data
respectively using the Gaussian Process. The distance duality relation is
checked by a non-parametric reconstruction using the reconstructed $H$, $d_L$,
and the volume-averaged distance $D_v$. We compare the results obtained for
different choices of the covariance function employed in the Gaussian Process.
It is observed that the theoretical distance duality relation is in well
agreement with the present analysis in 2$\sigma$ for the overlapping redshift
domain $0 \leq z \leq 2$ of the reconstruction.
