Relation Consistency Theory: A Unified Geometric Framework for Cosmogenesis and Epochal Evolution

Standard cosmological models, while empirically robust, rely on disconnected theoretical frameworks to explain the distinct epochs of the universe. Primordial inflation, matter-dominated deceleration, and late-stage dark energy acceleration are traditionally modeled using separate, compartmentalized mechanisms (e. g. , Inflaton fields, ). This paper introduces Relation Consistency Theory (RCT), a purely geometric model of cosmogenesis that derives all macroscopic universal epochs from a single, continuous complex differential generator: d/d = ( () + i). By modeling the universe as a unified complex state that bifurcates into orthogonal standard and anti-phase relations, we mathematically eliminate the need for hardcoded initial mass or energy. The observable cosmic scale emerges natively as the dimensionless invariant C = u² + v². Calibrating the fundamental expansion field () to modern astronomical data (₀=0. 5616, =0. 3143, _=0. 0643) perfectly recovers the three observed cosmological eras. The model accurately predicts the epochal transition to dark energy at 9. 8 Gyr, cleanly resolves to a present-day Hubble Constant of H₀ = 70. 0 km/s/Mpc with a deceleration parameter of q₀ = -0. 55, and mathematically proves an asymptotic deep-future limit equivalent to a de Sitter universe (q -1). Furthermore, RCT resolves the early structure anomaly observed by JWST, proving that an exponential decay in early expansion geometrically forces rapid phase-locking, allowing massive galaxies to form within the first 500 million years.