A UV–IR Fractal Bridge from UFQFT to Cosmological Power Spectrum Suppression

We present a concrete ultraviolet–infrared (UV–IR) bridge connecting the Unified Fractal Quantum
Field Theory (UFQFT) to observable cosmological structure. In UFQFT, spacetime is intrinsically
fractal with an effective dimension D≈2.7 at microscopic (UV) scales, where particles emerge as
resonance configurations of coupled energy (Φ) and charge (Ψ) fields. We show that, under coarse-
graining, the theory exhibits a scale-dependent dimensional flow D(k)→3 toward macroscopic (IR)
regimes, recovering an effective quasi-classical geometry. Within this framework, we derive a modified
propagator of the form G(k)∼1/k2+ϵ(k), where ϵ(k)=D(k)−3 encodes the fractal deviation. This directly
leads to a suppression of the matter power spectrum, P(k)=PΛCDM(k) [1+(k/ktr)2]−ϵ, providing a natural
geometric origin for small-scale power suppression without invoking particle dark matter. The resulting
predictions are quantitatively testable with upcoming large-scale structure observations, particularly the
Euclid DR1 data release, offering a falsifiable pathway to connect fundamental fractal field dynamics
with cosmological measurements