Experimental Validation of Fractal Quantum Field Theory and the Study of Energy Models

This paper systematically investigates the experimental validation methods offractal quantum field theory (FQFT) and its applications in dark energy mod?els. Through the design of fractal Josephson junction experiments, Monte Carlosimulations to verify fractal heat kernel expansions, analysis of gravitational wavephase shift corrections induced by fractal effects, and fitting observational dataof dark energy models, the predictive power of FQFT is comprehensively tested.Experimental results show that the predictions of FQFT regarding the critical cur?rent scaling law, heat kernel expansion coefficients, and gravitational wave phasecorrections are in excellent agreement with experimental data, with an error mar?gin of less than 5%. The dark energy model fitting results indicate compatibil?ity between the fractal dimension parameter and the standard cosmological model(Df = 2.998 ± 0.008). This provides empirical support for the connection betweenfractal spacetime structures and dark energy. These findings not only confirm theself-consistency and reliability of FQFT but also lay an experimental foundationfor its applications in cosmology and quantum gravity research.Keywords: Fractal Quantum Field Theory; Experimental Validation; DarkEnergy Model; Fractal Josephson Junction; Gravitational Wave Phase Correction;Monte Carlo Simulation