Traditional simulations (e.g., Millennium, Illustris) impose a fixed background metric, whereas our framework allows the metric itself to evolve under fractal RG flows, modifying not only density fields but also causal and gravitational structure.
5. Implications for Galaxy and Filament Formation
The tidal torque theory (TTT), often invoked to explain angular momentum in galaxy formation, gains a new context:
 If initial conditions are inherently fractal and multiscale, then:
Angular momentum acquisition occurs not only from local overdensities but from entangled torque feedback across layers,
Galaxy spins exhibit long-range alignment patterns, which can persist beyond scales expected in CDM,
Filament axes trace RG flow fixed points, leading to preferred anisotropic directions observable in surveys like SKA and Euclid.
These predictions are testable via:
Angular correlation functions of spin axes,
Void-filament anisotropy distributions,
Directional dependence of large-scale gravitational potential fluctuations.
6. Link to Quantum Gravity and Statistical Physics
Finally, our integration aligns with recent trends in asymptotic safety approaches to quantum gravity, where:
Gravity flows toward a non-trivial UV fixed point,
The effective spacetime dimension flows from 4 in the IR to 2 in the UV (e.g., Reuter & Saueressig, 2012).
In our model, a similar dimensional flow occurs across cosmological layers, reflected in the effective Hausdorff dimension DHD_H, suggesting a cosmological analog of dimensional reduction observed in quantum gravity.
This bridges quantum spacetime emergence with observed LSS statistics, offering a powerful unification of scales, from Planck epoch fluctuations to galactic structure today.
C. No Singularities or Inflaton Fields Needed: Replaced by Structured Tunneling
1. Departure from Singularity-Centric Cosmologies
In conventional cosmology, the Big Bang singularity represents a breakdown of spacetime---where general relativity ceases to be predictive. Similarly, inflationary models, though powerful in explaining the flatness, horizon, and monopole problems, require:
