Typical H0H_0 variations of:
H02--4 km/s/Mpc\Delta H_0 \sim 2\text{--}4 \ \text{km/s/Mpc}
across directions separated by >60 on the sky, particularly at redshifts z0.5z \lesssim 0.5,
A dipolar anisotropy pattern in the H0eff(n^)H_0^{\text{eff}}(\hat{n}) map, aligned with the dominant layer tunneling vector or early-universe geometric asymmetry,
Statistical preference for higher local H0H_0 values in void-like regions, due to faster local expansion rates and earlier domain decoupling.
5. Observational Prospects
Already Hinted By:
Cosmicflows-3 and Pantheon+ datasets showing mild anisotropy,
Recent claims of hemispherical Hubble asymmetry (~3) by some supernova analyses.
Future Confirmations via:
Euclid's spectroscopic sample (~10 galaxies up to z2z \sim 2),
DESI's deep redshift catalog with angular resolution sufficient to trace anisotropies in radial BAO,
CMB lensing + LSS joint reconstructions to map the geometry of underlying domains.
6. Implications
Confirms a breakdown of the cosmological principle at the largest scales,
Provides a natural explanation for the Hubble tension without exotic dark energy,
Offers a quantifiable falsifiability target: a directional H0H_0 variance above a critical threshold (e.g., >1.5 km/s/Mpc> 1.5 \ \text{km/s/Mpc} rms across hemispheres) would be strong evidence against CDM and in favor of layered-fractal cosmology.
B. SKA: Anisotropic Spin--Filament Alignments Due to Fractal Torque
1. Background and Theoretical Setup
In standard CDM cosmology, tidal torque theory (TTT) describes how protogalaxies acquire spin from gravitational shear during structure formation. However, TTT assumes:
Gaussian random fields with homogenous statistics,
Single-scale collapse mechanics, and
A lack of persistent anisotropy beyond the linear regime.
In contrast, the fractal-layered cosmology introduces:
Nested domains of varying density and geometric curvature,
Scale-invariant fluctuations from renormalization group (RG) flows,
Persistent anisotropic tidal fields generated by asymmetric layer interfaces.
These produce non-Gaussian torques and directional bias in angular momentum acquisition---most notably, an alignment of galaxy spins with large-scale filamentary structures in an anisotropic and redshift-dependent fashion.
2. Model Mechanism
