Correlated large-scale structure alignments across regions with minimal causal contact,
Redshift-dependent anisotropies in supernova luminosity distances or baryon acoustic oscillation scales,
Gravitational lensing anomalies and non-Gaussian features traceable to phase-correlated mass distributions.
5. Mathematical Consistency and Embedding
This approach can be embedded in:
Topological quantum field theories (TQFT) extended over Lorentzian spacetimes,
Spin foam models or loop quantum cosmology, where quantum geometry is naturally phase-dependent,
A generalized AdS/CFT-type duality, where each cosmological layer is holographically dual to a boundary theory with encoded phase information.
C. Power Spectrum Comparison: Fractal P(k)k(3DH)P(k) \sim k^{-(3 - D_H)} vs. CDM's P(k)knsP(k) \sim k^{n_s}
The matter power spectrum P(k)P(k), which quantifies the variance of density fluctuations as a function of spatial scale (inverse wavenumber kk), offers a critical testbed for comparing standard cosmology with the proposed fractal-layered framework.
1. CDM Prediction
