One of the core tensions in modern cosmology is the Hubble tension---the discrepancy between:
Local measurements (e.g. via Cepheids and SNe Ia by SH0ES): H073 km/s/MpcH_0 \approx 73 \ \text{km/s/Mpc}, and
Early-universe inferences (e.g. Planck CDM fit): H067.4 km/s/MpcH_0 \approx 67.4 \ \text{km/s/Mpc}.
CDM assumes spatial uniformity in cosmic expansion, attributing any discrepancy to systematic errors. However, in the proposed fractal-layered cosmology, spatial and directional variations in H0H_0 naturally arise due to:
Fractal clustering and void-dominated geometry,
Layer-specific scale factor evolution ai(t)a_i(t),
Topological interference effects among adjacent regions.
Thus, H0H_0 becomes a direction-dependent observable, especially on Gpc scales.
2. Model Prediction
We define the effective local Hubble parameter in a given direction n^\hat{n} and redshift slice zz as:
H0eff(n^,z)=1a(n^,z)da(n^,z)dtt0H_0^{\text{eff}}(\hat{n}, z) = \frac{1}{a(\hat{n}, z)} \left. frac{da(\hat{n}, z)}{dt} \right|_{t_0}
This value is sensitive to:
Local density gradients due to void--wall transitions (LTB-like dynamics),
Interference in cosmic clock synchronization between layers,
Anisotropic phase alignment across nested domains.
3. Methodology for Detection
Euclid and DESI can probe these predictions through:
Angular-dependent BAO measurements: Variations in the angular diameter distance DA(z,n^)D_A(z, \hat{n}) and Hubble parameter H(z,n^)H(z, \hat{n}) across the sky,
Tomographic void mapping: Locating underdense regions and correlating them with local H0H_0 offsets,
Redshift drift analysis: Using Lyman- forest and high-z quasars to track small time variations in H(z)H(z),
Cross-correlation with large-scale CMB anomalies**: Testing for directional consistency in H0effH_0^{\text{eff}} gradients and CMB low- anomalies.
4. Quantitative Forecast
In our simulations, we observe:
