Constraining Cosmological and Galaxy Parameters using Strong
  Gravitational Lensing Systems
  Strong gravitational lensing along with the distance sum rule method can
constrain both cosmological parameters as well as density profiles of galaxies
without assuming any fiducial cosmological model. To constrain galaxy
parameters and cosmic curvature $(\Omega_{k0})$, we use the distance ratio data
from a recently compiled database of $161$ galactic scale strong lensing
systems. We use databases of supernovae type-Ia (Pantheon) and Gamma Ray Bursts
(GRBs) for calculating the luminosity distance. To study the model of the lens
galaxy, we consider a general lens model namely, the Extended Power-Law model.
Further, we take into account two different parametrisations of the mass
density power-law index $(\gamma)$ to study the dependence of $\gamma$ on
redshift. The best value of $\Omega_{k0}$ suggests a closed universe, though a
flat universe is accommodated at $68\%$ confidence level. We find that
parametrisations of $\gamma$ have a negligible impact on the best fit value of
the cosmic curvature parameter.
  Furthermore, measurement of time delay can be a promising cosmographic probe
via "time delay distance" that includes the ratio of distances between the
observer, the lens and the source. We again use the distance sum rule method
with time-delay distance dataset of H0LiCOW to put constraints on the Cosmic
Distance Duality Relation (CDDR) and the cosmic curvature parameter
$(\Omega_{k0})$. For this we consider two different redshift-dependent
parametrisations of the distance duality parameter $(\eta)$. The best fit value
of $\Omega_{k0}$ clearly indicates an open universe. However, a flat universe
can be accommodated at $95\%$ confidence level. Further, at $95\%$ confidence
level, no violation of CDDR is observed. We believe that a larger sample of
strong gravitational lensing systems is needed in order to improve the
constraints on the cosmic curvature and distance duality parameter.
