Ekpyrotic and cyclic models (Khoury et al., 2001),
Loop quantum cosmology (Ashtekar & Singh, 2011),
Matter bounce scenarios with modified gravity (Brandenberger et al.).
These typically address:
Singularity avoidance,
Natural generation of perturbations,
Homogeneity through pre-bounce contraction.
5. Points of Contact and Divergence
Our model does not rely on pre-existing spacetime to contract and bounce. Instead, the universe emerges as a quantum transition from a higher-layer vacuum --- leading to a cosmogenesis event without reversal symmetry.
6. Conclusion of Comparison
While all three approaches (black hole universes, bouncing cosmologies, and the present layered-fractal model) attempt to transcend the singular Big Bang and provide deeper structure to spacetime evolution, this proposal introduces:
A non-singular, holographically connected, fractal genesis,
A mathematically defined framework generating testable predictions,
A structure that accommodates observed anomalies while remaining falsifiable.
Thus, the present model can be seen as a synthesis --- maintaining the philosophical elegance of horizon-based emergence, the structure of hierarchical layering, and the predictive rigor required by modern observational cosmology.
B. Integration with Multiscale Structure Formation and RG Flow Cosmology
1. Motivation for Multiscale Modeling in Cosmology
The large-scale structure (LSS) of the universe exhibits fractal-like patterns, with filaments, voids, and walls forming across a wide range of scales. Traditional CDM cosmology, though successful at matching average two-point statistics, fails to capture:
The scale-invariant clustering seen in deep redshift surveys,
The void-hierarchy distribution,
The persistence of anisotropic filament alignments beyond the scale of statistical isotropy.
This calls for an explicitly multiscale model, where structure emerges not from a single inflationary field but from recursive dynamics across hierarchical layers.
2. RG Flow as Cosmological Evolution
