Causal Memory Gravity: Cosmological Framework and Observational Tests

We present a comprehensive framework for Causal Memory Gravity (CMG), an infrared modifi-cation of general relativity in which late-time cosmological dynamics are governed by the collectivememory response of spacetime to energy-momentum perturbations. The effective action contains anonlocal memory kernel (□ + β2)−1 acting on the Ricci scalar, introducing two phenomenologicalparameters: the coupling strength α and the memory relaxation rate β. We derive ghost-free con-ditions (−β2 < α < 0), analyze cosmological evolution, and demonstrate that CMG preserves theacoustic structure of the cosmic microwave background while modifying late-time structure growth.For fiducial parameters β ∼ H0 and α = −0.3β2, the theory predicts S8 ≃ 0.77–0.78, resolvingthe tension between Planck and weak lensing measurements. A natural screening mechanism basedon environment-dependent memory relaxation ensures compliance with Solar System tests and theGW170817 constraint cGW = c without introducing additional free parameters. The frameworkis falsifiable via the β-universality hypothesis: the memory parameter must be consistent acrossindependent measurements from supernova distances, CMB polarization, and structure growth. Wedevelop a complete statistical methodology for testing this prediction and discuss observationalprospects with DESI, Euclid, and CMB-S4. This paper focuses exclusively on cosmological appli-cations; galactic dynamics and ultraviolet aspects are deferred to companion works.