i(r)rDH,i3\rho_i(r) \sim r^{D_{H,i} - 3},
ij\alpha_{ij} represents coupling strength between layers ii and jj,
i\theta_i are phase variables encoding entanglement or topological mismatch.
This equation reflects:
Inhomogeneous expansion, driven by density gradients,
Topological interference, which may induce localized acceleration or deceleration,
Violation of cosmic homogeneity, consistent with observational anomalies.
3. Implementation Strategy
We modify the background evolution module of CLASS to read a tabulated fractal density profile (r)\rho(r), parametrized by observationally informed values of DH[2.0,2.6]D_H \in [2.0, 2.6],
Apply a spatial grid slicing r[0,4 Gpc]r \in [0, 4\text{ Gpc}] into multiple concentric shells representing "cosmic layers,"
For each shell:
