STUDIES IN GRAVITATIONAL LENSING: THE REDSHIFT DIFFERENCE, COSMOLOGICAL INFERENCE, AND COMPUTATIONAL APPROACHES

Abstract

In this thesis, I focus on the redshift difference between two images in gravitational lensing systems and assess the capability to detect these differences. Due to photons travelling along distinct paths in such systems, the emission times differ if observed simultaneously. Consequently, this results in observable redshift differences. I have quantified the magnitude of this redshift difference and evaluated the potential of using the ELT to detect it with the aid of the ANDES Calculator. Furthermore, I have calculated the redshift drift at the source redshift for seven real gravitational lenses, finding that the results align well with predictions from the \Lambda CDM model. Additionally, considering the sources are moving with the Hubble flow, there is a corresponding shift in flux over time. I have estimated the magnitude of this flux drift and compared it with the detection capabilities of the SKA. Moreover, lux drift is another phenomenon associated with redshift drift. As celestial bodies move with the Hubble flow, the flux from distant objects gradually evolves, providing a direct test of cosmological models. With advancements like SKA II, we anticipate being able to measure this subtle flux change in the future. Our research investigates strategies for detecting flux drift and demonstrates the feasibility of directly observing cosmological expansion through this signal. We find that if the stability of the flux is maintained at a level of \Delta F/F \sim 10^{-6}, then the SKA 1-mid Array should be capable of detecting these effects. In parallel to the above studies, I have developed a new gravitational lensing package using the Julia programming language. I have completed a portion of the image simulation, covering both parametric and pixelized sources. My future work will focus on completing the I/O module and the sampling module of this package.