Topological interference modeled via phase-entanglement between layers.
Power spectrum comparison: Fractal P(k)k(3DH)P(k) \sim k^{-(3-D_H)} vs. \LambdaCDM's P(k)knsP(k) \sim k^{n_s}.
4. Numerical Simulations
Hubble parameter variation H(r)H(r): Layer-dependent evolution from CLASS-fractal extension.
Galaxy spin correlations: Tidal torque simulations with fractal initial perturbations.
CMB anisotropies: Ray-tracing through multilayer spacetime geometries.
5. Observable Predictions
Euclid/DESI: Spatial and directional H0H_0 gradients.
SKA: Anisotropic spin-filament alignments due to fractal torque.
JWST: Abundance and mass function of early galaxies from fractal collapse.
LISA: Echoes from geodesic scattering at layer boundaries.
6. Discussion
Comparison with black-hole universe models and bouncing cosmologies.
No singularities or inflaton fields needed: replaced by structured tunneling.
Experimental constraints: Strong lensing, redshift drift, and tensor mode forecasts.
Theoretical robustness:
Stability of multi-layer configuration,
Validity under Swampland Conjecture.
7. Conclusion
Summary of resolved cosmological tensions and proposed tests.
Future prospects:
21cm tomography,
Cosmic shear lensing,
Phase-correlated gravitational wave backgrounds.
I. Introduction
A. The Three Persistent Problems in Contemporary Cosmology
Despite the remarkable success of the CDM model in explaining a broad range of cosmological observations, several persistent anomalies suggest the need for theoretical refinement or potentially a paradigm shift. We highlight three of the most pressing issues that challenge the standard cosmological model:
(i) The Hubble Constant Discrepancy
A well-documented tension has emerged between local and early-universe measurements of the Hubble constant H0H_0. Direct measurements using Cepheid-calibrated Type Ia supernovae (e.g., SH0ES collaboration) yield H073.01.0km/s/MpcH_0 \approx 73.0 \pm 1.0 \, \text{km/s/Mpc} [1], while inference from Planck CMB observations assuming the CDM model gives H067.40.5km/s/MpcH_0 \approx 67.4 \pm 0.5 \, \text{km/s/Mpc} [2]. This ~5 tension is statistically significant and cannot be easily attributed to systematics alone [3].
Proposed resolutions fall into two main categories: early-time modifications (e.g., early dark energy [4]) and late-time effects such as local voids [5] or inhomogeneous expansion [6]. However, none has yet provided a fully self-consistent, predictive, and observationally supported solution across all scales.
