1. Purpose and Methodology
To capture the implications of the proposed layered fractal cosmology, we develop a numerical extension of the CLASS Boltzmann code (Cosmic Linear Anisotropy Solving System), tailored to accommodate radially-dependent density fields and interlayer coupling effects. The key objective is to simulate a non-uniform Hubble parameter H(r)H(r) that evolves differently in each cosmic layer.
We incorporate three core features:
Fractal energy density scaling: (r)rDH3\rho(r) \sim r^{D_H - 3},
Modified Friedmann equation with interlayer potential terms,
Void-dominated boundary conditions replacing uniform background assumptions.
2. The Modified Friedmann Equation with Spatial Dependency
Each radial layer ii evolves according to:
Hi2(r)=8G3i(r)kiai2+jiijcos(ij)H_i^2(r) = \frac{8\pi G}{3} \rho_i(r) - \frac{k_i}{a_i^2} + \epsilon \sum_{j \ne i} \alpha_{ij} \cos(\theta_i - \theta_j)
Where:
Hi(r)H_i(r) is the Hubble rate in layer ii,
