The Horizon Expansion Fractal: A Unified Framework For General Relativity, Loop Quantum Gravity, and Cosmic Expansion

The unification of general relativity (GR) and quantum mechanics remains one of the most fundamental challenges in theoretical physics. In this paper, I propose the Horizon Expansion Fractal (HEF) model, a novel recursive geometric framework that integrates space-time dynamics across quantum and cosmological scales. The HEF model is defined by a self-similar fractal transformation, governed by a scaling function dependent on the Hubble parameter, a beta function regulating rotational decay over cosmic time, and an escape radius linked to cosmic expansion. These recursive transformations define an emergent discrete space-time structure, aligning with principles from loop quantum gravity (LQG), spin foam models, and holographic dualities.