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 coarsegraining, 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/k 2+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.

A growing body of observational and theoretical evidence suggests that fractal geometry is not an anomaly but a recurring structural principle across the Universe, manifesting consistently from cosmological scales to quantum phenomena. Large-scale galaxy distributions, dark matter clustering, interstellar media, turbulent flows, biological networks, and quantum paths all exhibit scale-invariant, hierarchical organization characterized by non-integer fractal dimensions. In this work, we present a comprehensive, multi-scale analysis of fractal structures in nature and demonstrate that a critical Hausdorff dimension in the range D≈2.6-2.8, with a pronounced convergence near D≈2.7, emerges repeatedly across disparate physical systems. We argue that this convergence is not coincidental but reflects a fundamental geometric balance between localization and delocalization, enabling stable structures, long-range interactions, and temporal evolution. Interpreting these findings within the Unified Fractal Quantum Field Theory (UFQFT) framework, we propose that spacetime itself possesses an intrinsic fractal architecture, with matter, dark matter, and dark energy corresponding to distinct resonance regimes of unified energy-charge fields embedded in this geometry. The value D≈2.7 is identified as a critical threshold at which particle stability, confinement, propagating fields, and the arrow of time coexist. This perspective offers a unifying geometric interpretation of structures and dynamics across physical scales and provides concrete, testable predictions for cosmology, particle physics, and quantum phenomena.

Unified Fractal Quantum Field Theory (UFQFT) proposes that the fundamental structure of spacetime is not characterized by an integer dimension but by a critical fractal Hausdorff dimension that governs the formation of stable physical reality. In this framework, the Hausdorff dimension D does not represent the number of spatial dimensions but quantifies the degree of connectivity, confinement, and resonance of unified energy (Φ) and charge (Ψ) fields within spacetime. We demonstrate that a critical threshold at D≈2.7 uniquely permits the emergence of stable standing-wave resonances identified as elementary particles, while simultaneously allowing long-range interactions and a non-frozen temporal evolution. For D=3, field delocalization prevents confinement and particle formation, whereas for significantly lower values of D, excessive localization suppresses interaction range and halts dynamical evolution. The value D≈2.7 thus represents a geometric balance point between localization and dispersion, enabling quark confinement, lepton and photon propagation, and the continuous flow of time. Within this scheme, normal matter corresponds to resonances near the critical dimension, dark matter emerges from subcritical fractal regimes incapable of full particle formation, and dark energy arises as the asymptotic D→3 limit of delocalized field oscillations. The theory yields testable predictions for particle stability thresholds, mass hierarchies, confinement scales, and cosmological structure formation, offering a unified geometric explanation for matter, time, and the dark sector based on a single fractal parameter.

A document by haci Sogukpinar. Click on the document to view its contents.

The conventional picture of baryogenesis faces the challenge of explaining how an initially symmetric early universe produced the observed matter-antimatter asymmetry. In this work, we introduce a resonance-selective mechanism based on the Unified Fractal Quantum Field Theory (UFQFT), in which particles are modeled as geometric resonances of unified energy-charge fields in a fractal spacetime. We show that, contrary to the expectation of complete annihilation, non-identical matter-antimatter pairs (such as proton-antineutron or neutron-antiproton) do not fully convert into photons. Instead, they undergo fractal-resonant reconstruction, generating mesonic and baryonic intermediate states that preferentially collapse into stable matter resonances. Identical pairs (e.g., proton-antiproton) annihilate completely, but mixed pairs produce asymmetric decay chains. Even with equal initial population of baryons and antibaryons, this selective annihilation dynamically favors matter over antimatter during the first microseconds of cosmic evolution. We argue that this mechanism provides a natural, geometrydriven explanation for the matter-dominated universe without requiring fine-tuned CP violation.

A document by haci Sogukpinar. Click on the document to view its contents.

We propose a unified framework in which the vacuum is not empty but constituted by a non-material, fractal "dark-energy ocean" composed of fundamental energy (Φ) and charge (Ψ) fields in non-integer dimensional spacetime. These fields represent non-condensed, neutral resonance modes that do not form ordinary matter but set the minimum resonance background of the Universe. Light is described as a propagating Φ-Ψ resonance configuration, and electromagnetic radiation emerges from local oscillatory modulations of this fractal energy-charge medium.

This work presents a geometric reinterpretation of gravity within a fractal field governed by a fixed spacetime dimension D = 2.7 and proposes, within the framework of Unified Fractal Quantum Field Theory (UFQFT), that the gravitational force arises from the intrinsic curvature of the unified energycharge field (Φ-Ψ) rather than from an independent fundamental force. Using a reference scale of r0 = 0.1 mm, where classical and fractal gravity coincide, the model is fully consistent with macroscopic experiments, and a geometric scaling factor (r0/r) of 0.7 allows for a smooth strengthening of gravitational coupling into the atomic and nuclear regimes, suggesting that the fractal field can be transformed into an electromagnetic field at the atomic scale and a nuclear force at the nuclear scale. Analytical formulations for the fractal-corrected potential, acceleration, and energy density show that this fixed-dimensional geometry produces continuous power-law amplification on small scales without violating current experimental limits, and the resulting "Fractal Compression Mechanism" naturally explains the apparent divergence between gravitational and nuclear forces as different manifestations of the same geometric structure, implying that nuclear interactions arise as resonant boundaries of the compressed spacetime curvature.This framework thus appears to provide a unified, scale-invariant description of the fundamental interactions within a single fractal spacetime continuum.

In this study, we demonstrate that Einstein's General Relativity (GR) emerges as the classical geometric limit of the Unified Fractal Quantum Field Theory (UFQFT). Within UFQFT, spacetime is defined as a scale-dependent fractal manifold characterized by a local dimension D(x), and all physical interactions arise from the resonant dynamics of two unified fundamental fields: the energy field (Φ) and the charge field (Ψ). The macroscopic curvature of spacetime, expressed by Einstein's field equations, is shown to result from the collective resonance geometry of these fields when D→3.0. Gravitation is reinterpreted as an emergent resonance curvature of the Φ-field, rather than a fundamental force. The classical energymomentum tensor Tμν is replaced by a fractal energy tensor Tμν (Φ,Ψ,D) which depends explicitly on the local fractal dimension. This framework naturally incorporates dark matter as baryon-free, neutral resonance structures of the Φ-Ψ fields trapped in sub-fractal domains (D<3), and dark energy as nonmaterial vacuum resonances (Φ₀ modes) that maintain constant phase and contribute to cosmic expansion. The results indicate that General Relativity is not an independent postulate but a macroscopic manifestation of a deeper fractal field dynamics. This correspondence provides a unified geometric interpretation of spacetime curvature, particle interactions, and cosmological acceleration within a single theoretical framework.

This study investigates the emergence of relativistic phenomena such as time dilation, length contraction, and spacetime curvature within the theoretical framework of Unified Fractal Quantum Field Theory (UFQFT). Unlike Einstein's continuous spacetime geometry, UFQFT assumes that spacetime itself is a dynamic fractal resonance field generated by bound energy (Φ) and charge (Ψ) fields. The local fractal dimension (D) provides a geometric origin for relativistic effects, acting as a variable governing both temporal flow and spatial scaling. As the energy density or gravitational potential increases, the local fractal structure compresses (D↑) and decreases its intrinsic resonant frequency, which subsequently leads to the phenomena of time dilation and spatial distance contraction. Mathematically, this study establishes the relationship between Lorentz transformations and fractal scaling relations, showing that the classical Lorentz factor 𝛾 = (1 − 𝑣 2 /𝑐 2) −1/2 can be reformulated as a ratio of fractal dimensions, , 𝛾 ↔ √𝐷′/𝐷 0. while the gravitational curvature and field resonance density are unified by deriving the Einstein curvature tensor Gμν as a macroscopic limit of the Φ-Ψ resonance tensor. Observational inferences can be verified experimentally by investigating them through high-precision systems such as GPS satellite synchronization, gravitational redshift in atomic clocks, and gravitational interferometry. The results show that the relativistic corrections measured in these systems can be interpreted as local modulations of the spacetime fractal dimension rather than metric curvature, and the proposed framework extends general relativity by placing it in a larger, scaledependent geometric context and offers a coherent bridge between macroscopic relativity and microscopic quantum structure.

The Unified Fractal Quantum Field Theory (UFQFT) has been proposed as a geometric framework in which matter, interactions, and cosmology emerge from resonance states of unified energy (Φ) and charge (Ψ) fields embedded in a fractal spacetime of effective dimension D≈2.70. While recent studies have demonstrated the potential of UFQFT to explain particle stability, quark confinement, neutrino oscillations, and dark sector phenomena, several critical aspects remain undeveloped. In this work, we address these open challenges by introducing a quantization scheme for the fractal dimension D, exploring microscopic origins of the fractal potential V(D), and formulating propagators and renormalization within fractal quantum field theory. Furthermore, we analyze the emergence of Standard Model-like gauge symmetries from higher-order fractal structures, discuss compatibility with Higgs phenomenology, and compare UFQFT predictions with electroweak precision data and collider observables. We also refine the mechanisms of baryogenesis and CP violation in terms of dimensional fluctuations, and provide updated cosmological implications, including CMB signatures and non-Gaussianity constraints testable by upcoming surveys. By systematically extending UFQFT in these directions, we aim to establish it as a more predictive and experimentally falsifiable alternative to the Standard Model and ΛCDM cosmology.

The Unified Fractal Quantum Field Theory (UFQFT) provides a novel framework in which all fundamental particles and interactions emerge as resonances of unified energy (Φ) and charge (Ψ) fields within a fractal spacetime of dimension approximately D ≈ 2.7. This approach offers a coherent description of particle properties, nuclear processes, and cosmological phenomena as manifestations of underlying fractal geometries. UFQFT makes experimentally testable predictions across multiple scales, from micro-scale particle physics experiments and nuclear decay processes to macro-scale astrophysical and cosmological observations, including gravitational waves, cosmic microwave background anomalies, and dark matter/energy distributions. By unifying these domains, UFQFT has the potential to address unresolved issues in the Standard Model, provide insight into the nature of dark matter and dark energy, and offer explanations for observed cosmological anomalies, establishing a framework for comprehensive experimental validation.