Holographic Relative Density as Unified Origin of Dark Matter and Dark Energy

The current standard cosmological model (ΛCDM) successfully describes cosmic acceleration and galactic rotation curves, yet the nature of dark energy and dark matter remains a major mystery. This paper, building on the relative density holographic gravity theory [1], proposes a particle-free unified explanation: sparse spacetime (low δ, volume-law entanglement entropy dominant) requires additional positive curvature compensation to maintain holographic information encoding consistency. This compensation mechanism produces net extra gravitational wells in galactic outskirts (gradient repulsion suppressed by slow gradients, curvature attraction dominant), simulating dark matter effects; on large scales with average sparsity, it dominates repulsion, driving cosmic acceleration (dark energy). This emergent explanation arises from the mismatch between area-law and volume-law entanglement entropy, requiring no additional fields or particles, relying solely on the original model's macroscopic density parameter δ and lowest-order modification to the Einstein field equations. Order-of-magnitude estimates show consistency with observed dark matter density (~10^{-24} g/cm³ in galactic halos) and cosmological constant (~10^{-122} ℓ_P^{-2}). The model retains the original theory's laboratory testability and provides new predictions for future astronomical observations (e.g., Euclid/JWST on void and cluster curvature distributions).