Resolving the S8 Tension in Ramanujan Background-Interval Cosmology

Abstract

The discrepancy between the amplitude of matter fluctuations, S8S8, measured by weak lensing surveys and that inferred from the cosmic microwave background (CMB) by the Planck satellite has reached the 2−3σ2−3σ level. We propose a resolution to this tension utilizing the Ramanujan Background-Interval Cosmology (RBIC) framework. While previous work (Paper 4) demonstrated that background modifications governed by the parameter α0α0 can resolve the H0H0 tension, here we show that scale-dependent interval perturbations, parameterized by an interval coupling κ~ΨIκ~ΨI, naturally suppress structure growth at small scales without altering the successful CMB predictions. Using compressed likelihoods from the Dark Energy Survey (DES Y3) and the Kilo-Degree Survey (KiDS-1000), we constrain the interval coupling to κ~ΨI=0.12±0.02κ~ΨI=0.12±0.02. Furthermore, the inclusion of the recent KiDS-Legacy (2025) data, which observes a higher S8S8 value, effectively reduces the required coupling, demonstrating the flexibility and observational consistency of the RBIC framework.