The Local Hammer of Precision Cosmology: Analysis of Weak-Lensing Statistics

Abstract

Modern cosmology is now going through a scientific revolution towards the realm of high-precision cosmology. The local environment plays a significant role in achieving precision cosmology and refining our understanding of the formation and evolution of the universe. Whilst the underlying assumption of the \textit{FLRW} cosmological model is that matter is homogeneously distributed throughout the universe, gravitational influences over the life of the universe have resulted in mass clustered on a range of scales. In our inhomogeneous universe, the view of an observer could be influenced by the location and local environment. In this thesis, we descriptively analyse the influence of the local environment on weak-lensing (WL) signals and find out the optimal solution to mitigate this effect to achieve precision cosmology. We develop a ray tracing algorithm, solve null geodesic equations, measure various WL properties by setting observers in different regions of cosmic structures, and analyse how the WL signals are changing due to the positions of the observers in the large-scale structure (LSS). We find that the amplitudes of the characteristic curves are getting higher in denser areas as compared to the low density areas. We constrain cosmological parameters and find that the local environment influences the WL statistics at low redshifts, and this effect fades as light travels towards higher redshifts. The most important outcome of this thesis demonstrates that the minimal redshift for constraining cosmological parameter $\Omega_{\rm m}$ ($H_0$) is $z \sim 0.2$ $(z \sim 0.6 )$, and above this redshift the effect of the local environment is negligible. Additionally, the WL shear is not sensitive to Hubble parameter $H_0$, and the non-Gaussian parameter $f_{\rm NL}$ for the squeezed bispectra configuration of WL shear is not impacted by the local environment. The outcomes of this thesis can add percent-level precision to measure data from future LSS and WL surveys.