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 zₙorm ≥ 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).