The cosmic imprint of time : decoding the evolving cosmos through weak gravitational lensing

A persistent discrepancy known as the S₈ tension challenges standard cosmology: weak-lensing measurements prefer less large-scale structure clustering than predicted by extrapolating cosmic microwave background (CMB) constraints to the late Universe. It may arise from observational systematics, astrophysical processes, or new dark-sector physics. Using cosmic shear data from KiDS-1000 and DES-Y3, I investigate whether changes to the halo mass function can explain the tension. The data prefer approximately 30 percent fewer halos above 100 trillion solar masses, implying a roughly 25 percent suppression of the matter power spectrum on scales of 10 megaparsecs. This resolves the S₈ tension but conflicts with independent cluster-abundance and baryonic-feedback constraints, highlighting the need to diagnose inference systematics before invoking new physics. To address projection degeneracies in weak lensing, I develop an inference framework based on the Bernardeau-Nishimichi-Taruya (BNT) transform. It reorganizes lensing kernels to localize contributions in redshift and physical scale, mapping angular-scale observables to well-defined three-dimensional physical scales. The resulting pipeline produces stable, unbiased S₈ constraints while retaining strong constraining power. Because redshift separation is sensitive to intrinsic alignments (IA), a contaminant of cosmological shear signals, I test the framework under non-zero IA. It remains unbiased when the assumed IA model reasonably describes the signal. I also introduce model-independent physical-scale and redshift-slicing diagnostics that reveal the scale and redshift dependence of IA, with broader applications to other observational systematics. Finally, using KiDS-Legacy data, I perform the first physical-scale-based cosmic shear analysis. Removing contributions from nonlinear scales yields an S₈ posterior centred on 0.798. This agrees with the fiducial KiDS bandpower and uncut pseudo-angular-power-spectrum constraints, indicating that nonlinear feedback does not significantly bias current inference. An alternative covariance prescription reveals a mild tendency toward lower S₈ on larger physical scales, suggesting a potentially important survey-pipeline systematic. BNT-based physical-scale cuts therefore both mitigate nonlinear systematics and test the internal consistency of weak-lensing pipelines.