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