Spectral Temporal Memory in Gravity: Scale-Dependent Growth and the S₈ Tension (Paper XLIII)

This repository contains the numerical code, data, and manuscript for the Spectral History-Dependent Gravity (HDG) framework, a modification of gravitational dynamics based on spectral temporal memory. The effective gravitational coupling becomes a non-local operator in time, leading to scale-dependent suppression of structure growth at late times (z < 1) while preserving standard cosmology at recombination. Key results:• Best-fit parameters: (A, α, γ, μ₀) = (0.5, 1.2, 1.7, 9.0)• Statistical improvement: Δχ² = 3.39 relative to ΛCDM (fit to RSD data)• σ₈ reduction: 7.25% (stable for normalization redshift z_norm ≥ 10)• Predicted S₈ = 0.772, in excellent agreement with DES Y3 (0.776 ± 0.017) and KiDS-1000 (0.766 ± 0.020) The framework naturally resolves the S₈ tension between CMB (Planck) and weak lensing measurements without introducing new dynamical degrees of freedom. The multiplicative UV-screening implementation ensures General Relativity is recovered at large scales (k → 0) and early epochs (z ≳ 3), while suppressing growth on non-linear scales at late times. This work provides falsifiable predictions for upcoming surveys (DESI, Euclid, LSST) through scale-dependent signatures in fσ₈(k, z).