A non-parametric test of variability of Type Ia supernovae luminosity
  and CDDR
  The first observational evidence for cosmic acceleration appeared from Type
Ia supernovae (SNe Type Ia) Hubble diagram from two different groups. However,
the empirical treatment of SNe Type Ia and their ability to show cosmic
acceleration have been the subject of some debate in the literature. In this
work we probe the assumption of redshift-independent absolute magnitude
$(M_{\mathrm{B}})$ of SNe along with its correlation with spatial curvature
($\Omega_{k0}$) and cosmic distance duality relation (CDDR) parameter
($\eta(z)$). This work is divided into two parts. Firstly, we check the
validity of CDDR which relates the luminosity distance ($d_L$) and angular
diameter distance ($d_A$) via redshift. We use the Pantheon SNe Ia dataset
combined with the $H(z)$ measurements derived from the cosmic chronometers.
Further, four different redshift-dependent parametrizations of the distance
duality parameter $(\eta(z))$ are used. The CDDR is fairly consistent for
almost every parametrization within a $2\sigma$ confidence level in both flat
and a non-flat universe. In the second part, we assume the validity of CDDR and
emphasize on the variability of $M_{\mathrm{B}}$ and its correlation with
$\Omega_{k0}$. We choose four different redshift-dependent parametrizations of
$M_{\mathrm{B}}$. The results indicate no evolution of $M_{\mathrm{B}}$ within
$2\sigma$ confidence level. For all parametrizations, the best fit value of
$\Omega_{k0}$ indicates a flat universe at $2\sigma$ confidence level. However
a mild inclination towards a non flat universe is also observed. We have also
examined the dependence of the results on the choice of different priors for
$H_0$.
