ψ-Retention as a Retentive Regime of Large-Scale Structure

This work introduces ψ-Retention as a retentive regime of Large-Scale Structure (LSS), motivated by recent observations indicating suppressed growth at low redshift, including a plateau in fσ8, a growth index γ ≈ 0.64, and emerging signs of topological stability. In this framework, cosmic structure approaches a state of effective topological persistence, where large-scale reconfiguration becomes negligible while cosmic expansion continues. The paper defines operational conditions for this regime using Betti numbers, filament characteristics, and void profiles. ψ-Retention provides a structural interpretation of late-time cosmology that complements existing approaches such as Modified Gravity and Dynamical Dark Energy, focusing on the state of the system rather than the underlying mechanism. The framework is testable with current and upcoming cosmological surveys, including Euclid and DESI, through measurements of growth rate plateau, topological stability, and structural invariance.