ψ-Retention Cosmology II: Λψ — A RetentionTerm for the Large-Scale Structure

This article develops ψ-Retention Cosmology II: Λψ — a retentional term supplementing the standard cosmological constant Λ and redefining the stability of the large-scale universe. Within ψ-architecture, difference (Δψ) and structural nodes (Ξ) stabilize form beyond flux, producing a residual, non-dissipative energy of retention that persists when motion ceases. Λψ expresses this equilibrium energy of stillness and modifies the Friedmann equations accordingly. The work derives the ψ-modified cosmological dynamics, identifies three regimes of retentional behavior (Λ-like equilibrium, soft drift, and patchy retention), and connects them with observational signatures in structure growth and weak lensing. Laboratory analogues in optical and acoustic interferometers reproduce plateau dynamics on smaller scales, confirming that Λψ is experimentally reproducible in principle. Thermodynamically, ψ-Retention Cosmology separates dynamic from retentional energy, defining a finite remainder of stability that echoes as the macroscopic Λψ. Philosophically, the paper continues the ψ-series — ψ-Silence (reproducibility without events), ψ-Potential (residual field), and ψ-Retention Cosmology (Λψ, cosmic retention). Together they articulate a retentional physics where stability, persistence, and reproducibility replace flux and action as the ground of being. Λψ thus unifies cosmology, experimental reproducibility, and the ethics of observation, advancing a philosophy of science centered on non-violation: maximizing information with minimal disturbance. Part of the ψ-Architecture Research Series (Volumes I–II, 2025).