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 (Ωk0), 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 parametrizations of the mass density power-law index (γ) to study the dependence of γ on redshift. The best value of Ωk0 suggests a closed universe, though a flat universe is accommodated at 68% confidence level. We find that parametrizations of γ 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 the "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 (Ωk0). For this we consider two different redshift-dependent parametrizations of the distance duality parameter (η). The best fit value of Ωk0 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.