Preliminary simulations yield the following key behaviors:
A monotonic radial gradient in H(r)H(r) with measurable plateaus corresponding to quasi-homogeneous layer interiors,
Sharp transitions in H(r)H(r) at layer boundaries coinciding with steep density shifts or void-like domains,
Effective Hubble tension reconciliation, with local measurements matching higher H0H_0, while deeper radial regions converge to lower global values.
Notably, the variation magnitude H6km/s/Mpc\Delta H \sim 6 \, \text{km/s/Mpc} is consistent with the observed discrepancy between local distance ladder and early-universe inference methods.
6. Implications
This simulation supports the following interpretations:
Layered topological structure can serve as a natural geometric regulator for the Hubble tension, without invoking exotic scalar fields or modified gravity,
The radial dependence of H(r)H(r) provides a physically meaningful parametrization for future BAO and redshift drift experiments,
Layer-specific HiH_i values can be directly mapped to void-centered cosmologies and inhomogeneous expansion models, while remaining embedded in a unified topological framework.
Simulations of a layer-dependent Hubble parameter H(r)H(r) grounded in fractal and topological cosmology reveal that local and global expansion rates can coexist within a coherent model. This framework not only accommodates the Hubble tension, but also links it to the structural features of a nested, anisotropic universe---offering testable predictions and theoretical robustness in the face of current cosmological puzzles.
IV.2. Fractal-Induced Angular Momentum Bias
Building upon the fractal matter distribution formalized in Section III.3 and its implications for early galaxy formation, we simulate how initial fractal inhomogeneities generate a statistical bias in galactic angular momentum orientations. This bias is framed not merely as a perturbation on isotropy, but as a macroscopic imprint of microscopic asymmetries seeded during the Blink Genesis (Section II.1) and structurally maintained by the multilayer topological scaffold (Section II.2).
1. Background and Motivation
Recent surveys---including Galaxy Zoo, Sloan Digital Sky Survey (SDSS), and Hyper Suprime-Cam---have detected mild but statistically significant parity-violating spin alignments across large cosmic volumes. These observations contradict the expectation of random, isotropic angular momentum distributions, as predicted by CDM in a statistically homogeneous and isotropic universe.
Our hypothesis: Fractal inhomogeneities in the primordial density field, as described by a non-integer Hausdorff dimension DHD_H, inherently break rotational symmetry on specific scales, leading to emergent spin alignment patterns due to anisotropic tidal torque accumulation.
2. Simulation Setup and Methodology
