P13: Weak Gravitational Lensing and the S8 Tension in BFUT: Why Late-Time Clustering Inference Is Not a Unique Test of Lambda-CDM

Weak gravitational lensing surveys - including KiDS, DES, and HSC - consistently measure a lower amplitude of matter fluctuations, parametrized by S8, than the value predicted by extrapolating the Planck CMB best-fit Lambda-CDM cosmology forward to the present epoch. This S8 tension is consistently measured at 2 to 3 σ significance across multiple independent surveys using different instruments, analysis pipelines, and sky regions, with some combined analyses reporting higher significance. Lambda-CDM treats this as an unexplained internal inconsistency requiring new physics, additional free parameters, or systematic uncertainties in the lensing analyses. A particularly important empirical pattern is that the low-S8 preference is strongest in low-redshift optical weak-lensing surveys, while higher-redshift CMB lensing measurements are generally closer to the Planck expectation. This suggests the discrepancy is tied to the late-time growth regime rather than to the primordial baseline itself, and it provides direct observational motivation for the redshift-dependent mechanism developed in Section 5. Importantly, the widely cited S8 value is not a direct observable but a compressed parameter inferred from shear correlations under specific modelling assumptions. The qualitative low-S8 trend across surveys may therefore be robust even when the exact numerical precision of the inferred value is less stable than often presented. This paper examines the S8 tension from within the Big Flare-Up Theory framework 9. BFUT proposes that the universe is infinite, non-expanding, and dynamically organized through gravitational sorting over indefinitely long timescales. In this framework, the apparent discrepancy between CMB-inferred and lensing-measured structure amplitudes is not a crisis requiring new physics. It is a natural signature of an ongoing, dynamically active cosmic web whose present-epoch clumpiness does not match the extrapolation of early-universe conditions through a finite-age expanding universe model. Furthermore, the S8 tension is identified as an internal contradiction within Lambda-CDM itself: the same Planck satellite that measures the CMB anisotropies also measures the SZ cluster abundance and CMB lensing, and these measurements are mutually inconsistent within the standard framework. BFUT's living-universe picture, in which structure grows continuously without a privileged starting epoch, provides a more natural context for the observed suppression of late-time structure growth relative to CMB predictions.