Gravitational Memory and the One Law: The Admittance Paradigm for Cosmic Evolution

Gravitational Memory and the One Law: The Admittance Paradigm for Cosmic Evolution This work presents the Gravitational Admittance Paradigm (GAP), a parameter-free framework for cosmic acceleration based on finite-response horizon thermodynamics rather than exotic matter fields. Mechanism: The vacuum sector evolves as a causal system with memory: cosmological horizons cannot instantaneously adjust their gravitational response to changes in expansion rate. Quantum information bounds (Margolus-Levitin theorem) and geometric accessibility constraints set a characteristic relaxation timescale. The macroscopic consequence is a delayed vacuum adjustment that naturally manifests as late-time cosmic acceleration. Key Results: Present-day vacuum fraction uniquely determined: $\Omega_{\Lambda,0} = 2\pi/9 \approx 0.698$ (no free parameters in dark energy sector) Early-universe consistency automatic: environmental monitoring enforces quantum Zeno suppression, ensuring BBN and CMB compatibility without fine-tuning Distinctive growth signature: a joint geometry-growth correlation ($H(z)$ vs. $f\sigma_8(z)$) provides falsifiable observational discriminant against $\Lambda$CDM and modified gravity Physical Foundation: The framework unifies three principles: (i) causality—horizons as finite-bandwidth information channels; (ii) quantum speed limits—bounding how fast vacuum states can evolve; (iii) holographic thermodynamics—relating entropy, temperature, and information processing capacity. The result is a single organizing principle—one law, multiple regimes—that governs vacuum response across all cosmic epochs without additional parameters or fields. Falsification Criteria: The model is excluded if (i) Planck+DESI data prefer $\Omega_{\Lambda,0}$ outside $[0.68, 0.72]$ at $3\sigma$; (ii) growth rate shows no $H(z)$-$f\sigma_8(z)$ correlation; (iii) CMB constraints require $\Omega_\Lambda(z \sim 1100) > 10^{-3}$. Status: Validated against DESI DR1 BAO data ($\chi^2/{\rm dof} = 0.28/7$, p-value $\approx 0.99$) with zero fitted parameters.