A Non-local Memory Extension of General Relativity: From Quantum Lindblad Dynamics to Galactic and Cosmological Phenomenology

We present a unified framework in which the dark matter and dark energy phenomena are interpreted as the macroscopic manifestation of a quantum memory field — the K¯arn¯amag tensor K µ ν . The theory is built upon a minimal extension of general relativity in which the Einstein equations are sourced by the sum of the baryonic stress-energy and K µ ν . The dynamics of the memory tensor are derived from a quantum Lindblad equation, where spacetime is treated as an open system interacting with a bath of Planck-scale causal horizons. The resulting Langevin equation, after noise averaging and taking the overdamped limit, reduces to a causal, density-dependent diffusion–decay equation. On galactic scales, the memory field is described by a convolution kernel whose parameters are not universal constants but emergent properties of a single fundamental function — the horizon density of states n h (I, H). Calibrating this function with only two galaxies (NGC 6503 and NGC 7331) yields a self-consistent prediction for a third galaxy (NGC 2403) that matches observational data. The same scaling relations naturally explain the dynamics of ultra-diffuse galaxies (NGC 1052-DF2) and the cores of dwarf galaxies (DDO 154) without fine-tuning, addressing long-standing tensions of the ΛCDM paradigm. To resolve multi-scale tensions, we promote the smoothing parameter to a dynamic “cosmic effective mass” m cosmo ( ρ b , z) driven by the background baryon density. This screening mechanism regularizes the memory accumulation in dense environments, successfully reconciling the framework with the early massive galaxies observed by JWST at z ∼ 10, and perfectly tracing the joint strong-and-weak lensing surface density profile (Σ(R)) of the massive cluster MACS J1206.2-0847 without cold dark matter particles. The model remains ghost-free, causal, recovers General Relativity in the Solar System via environmental screening, and offers a humble yet consistent exploration of non-local gravitational memory across galactic and cosmological scales.