The Cosmological Energy-Efficiency Cycle: From Free-State Dominance to Constrained Structures and Back

The universe evolves from an initial hot, dense state to the formation of structures—galaxies, stars, planets, life—and now undergoes accelerated expansion driven by dark energy. Despite detailed observations, a unified ontological account of this entire trajectory remains lacking. This paper develops an interpretation within Energy-Efficiency Theory (EET). Starting from Yang's Axioms, we propose that the universe follows a single, global Yang's Energy-Efficiency Cycle (YEC)—a five-stage dynamical paradigm (disturbance →→ response →→ stabilization →→ constraint →→ transition) governing the transformation of energy between free and constrained states, rather than a repetitive oscillation of spacetime. We derive the evolution equation for the constrained-state energy fraction fc=ρc/ρtotalfc=ρc/ρtotal directly from the three axioms, linking the structure formation rate ββ to the escape tendency λˉλˉ and the dissipation rate αα to the gravitational constraint barrier. The YEC stages are defined with quantifiable critical thresholds: disturbance (z>1030)(z>1030), response (1030>z>1100)(1030>z>1100), stabilization (1100>z>0.5)(1100>z>0.5), constraint (0.5>z>0)(0.5>z>0), transition (z