Revisiting the distance duality relation using a non-parametric
  regression method
  The interdependence of luminosity distance, $D_L$ and angular diameter
distance, $D_A$ given by the distance duality relation (DDR) is very
significant in observational cosmology. It is very closely tied with the
temperature- redshift relation of Cosmic Microwave Background (CMB) radiation.
Any deviation from $\eta(z)\equiv \frac{D_L}{D_A (1+z)^2} =1$ indicates a
possible emergence of new physics. Our aim in this work is to check the
consistency of these relations using a non-parametric regression method namely,
LOESS with SIMEX. This technique avoids dependency on the cosmological model
and works with a minimal set of assumptions. Further, to analyze the efficiency
of the methodology, we simulate a dataset of $200$ points of $\eta (z)$ data
based on a phenomenological model $\eta(z)= (1+z)^\epsilon$. The error on the
simulated data points is obtained by using the temperature of CMB radiation at
various redshifts. For testing the distance duality relation, we use the JLA
SNe Ia data for luminosity distances, while the angular diameter distances are
obtained from radio galaxies datasets. Since the DDR is linked with CMB
temperature - redshift relation, therefore we also use the CMB temperature data
to reconstruct $\eta (z)$. It is important to note that with CMB data, we are
able to study the evolution of DDR up to a very high redshift $ z = 2.418$. In
this analysis, we find no evidence of deviation from $\eta=1$ within a
$1\sigma$ region in the entire redshift range used in this analysis ($0 < z
\leq 2.418$).
