Fractal Entanglement Cosmology: Emergence of Geometry and Matter from Information Scaling

Modern cosmology faces persistent anomalies—the Hubble tension, the $¥sigma_8$ discrepancy, and the cosmological constant problem—suggesting that current models may overlook key aspects of spacetime and gravity. We propose a fractal entanglement cosmology in which geometry and energy density emerge from a dynamic field of local entanglement dimension, $D_t(¥mathbf{x})$. This field encodes how quantum information is distributed across spacetime, and its coarse-grained behavior gives rise to effective fractal dimensions for matter, $D_m(z)$, and spacetime, $D_v(z)$. Their difference, $D_{¥mathrm{eff}}(z)=D_m(z)-D_v(z)$, governs the evolution of the Hubble parameter $H(z)$ and energy density $¥rho(z)$. We show that entanglement localization induces oscillations in $D_{¥mathrm{eff}}(z)$, leading to deviations from $¥Lambda CDM$ predictions and a dynamic effective equation of state. This provides a natural explanation for the late-time constancy of $¥rho(z)$ without invoking fine-tuned vacuum energy. Comparing $H(z)$-derived $D_{¥mathrm{eff}}(z)$ to rotation-curve-based $D_{¥mathrm{eff}}^{¥mathrm{sim}}(z)$ from SPARC, KROSS, KMOS$^3$D, and DYNAMO, we find scale-consistent agreement. We performed simulations of baryon asymmetry during the inflationary and structure formation eras. Further, our simulations reveal that both dark energy and dark matter arise from the localization state of entanglement curvature, offering a unified interpretation of the dark sector. This framework provides an information-theoretic resolution to the cosmological constant problem and suggests that the Hubble tension reflects entanglement-driven dimensional transitions in the early universe.