The Gravitational Memory Principle for Cosmological Dynamics: Why Spacetime Cannot Be Markovian in an Entropy-Bounded Universe

Physical Context The standard cosmological model (ΛCDM) relies on a Markovian assumption where the vacuum energy density remains local and instantaneous. This framework examines the consequences of relaxing such an assumption. If the cosmological horizon is a boundary with finite entropy and finite information throughput, the gravitational response to expansion cannot be instantaneous. A retarded (non-Markovian) constitutive sector arises as a geometric necessity. Cosmic acceleration is then identified not as a dark energy field, but as the thermodynamic relaxation of the vacuum. Logic and Mechanism The principle of gravitational memory determines the vacuum evolution through a horizon admittance variable, η(t). This variable follows a driven relaxation equation where the forcing term is the kinematic expansion history. In the late-time regime, the dynamics are governed by a relaxation rate Γmem related to de Sitter quasinormal modes. Parameter-Free Prediction: The model determines the present-day vacuum density as ΩΛ,0=2π/9≈0.698. This value is a geometric consequence of the capacity of the horizon, requiring no fine-tuning or fitted constants. Causal Consistency: Environmental monitoring (Zeno suppression) ensures that the vacuum response remains negligible during the radiation-dominated era. This mechanism provides automatic compatibility with Big Bang Nucleosynthesis (BBN) and Cosmic Microwave Background (CMB) constraints. Observational Validation Validation against DESI DR1 Baryon Acoustic Oscillation (BAO) data yields a χ2/dof=0.28/7 (p-value ≈0.99) with zero adjusted parameters. The framework predicts a specific "thawing" equation of state, w(0)≃−0.92, and a mandatory correlation between the expansion history H(z) and the growth of structure fσ8(z). Falsification Criteria The framework is falsified if: The measurement of ΩΛ,0 deviates significantly from the 0.68−0.72 range. The equation of state is confirmed to be exactly −1 with sub-percent precision. The predicted geometry-growth correlation is absent in late-time surveys. The Gravitational Memory Principle replaces the ad hoc cosmological constant with a thermodynamic closure. It provides a minimalist, parameter-free description of the late-time universe, where acceleration is the inevitable macroscopic manifestation of horizon causality.