A Holographic Dual Explanation of Fractal Inflation and Dark Matter

Based on Fractal Holographic Emergent String Theory (FHEST), this studyproposes, for the first time, a unified model of inflation and dark matter within theframework of fractal spacetime. Through fractal AdS/CFT duality, the slow-rollparameters of the inflaton field are modulated by the fractal dimension dH, withcorrections that can explain the anomalies of the low-multipole moments in theCMB power spectrum. The mass spectrum of bound states of fractal D-branes alsoaligns with dark matter observations. Numerical fits indicate that, when the fractalparameter dH ∈ [1.2, 1.6], the theoretical predictions are consistent with Lyman-αforest data and the mass distribution of the Milky Way’s halo. Further predictedobservables, such as the fractal gravitational wave spectrum and jet anisotropicsignals, provide experimental pathways for verification.