Based on our simulations, we expect:
A mean alignment excess cos0.05--0.1\Delta \langle \cos \theta \rangle \sim 0.05\text{--}0.1 in preferred directions,
Higher-order angular modes (e.g., =2,4\ell = 2, 4) detectable in the multipole decomposition of spin alignments,
Anisotropic spin correlations reaching 3\sim 3 significance with 106\gtrsim 10^6 galaxies.
6. Implications
Direct evidence of non-Gaussian tidal fields inconsistent with CDM,
Supports the fractal-layered torque model and RG-induced anisotropy,
Opens possibility to constrain the cosmic layering vector field via observed spin maps,
Offers a non-CMB route to falsify or validate the new cosmological paradigm.
C. JWST: Abundance and Mass Function of Early Galaxies from Fractal Collapse
1. Context and Discrepancy in CDM
One of the most pressing challenges to CDM is the unexpected abundance of massive, mature galaxies at high redshift. JWST has already detected:
Galaxies at z>10z > 10 with stellar masses 1010M\gtrsim 10^{10} M_\odot,
Compact morphologies and enriched metallicity inconsistent with gradual CDM hierarchical growth,
A steep high-redshift mass function that overshoots standard semi-analytical models and N-body simulations.
This raises questions about:
The timeline of structure formation,
The efficiency of baryon cooling and star formation,
The initial fluctuation spectrum and background expansion history.
2. Fractal Collapse Mechanism
In the proposed fractal-layered cosmology, early galaxy formation is enhanced due to:
Multiscale gravitational focusing from nested curvature layers,
Phase interference between geometric layers that amplify overdensities at selected radii rir_i,
A non-Gaussian initial spectrum where the fractal dimension DH>3D_H > 3 at early epochs.
The matter overdensity evolution follows:
(r,t)a(t)f(DH)rDH3\delta(r, t) \propto a(t)^{f(D_H)} \cdot r^{D_H - 3}
