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<0)(z<0). The framework quantitatively recovers the Hubble constant H0=71.5±1.2H0=71.5±1.2 km/s/Mpc, the CMB power spectrum (ns=0.965±0.005,r=0.03±0.01)(ns=0.965±0.005,r=0.03±0.01), BAO scale, primordial nucleosynthesis abundances (Yp=0.248±0.002)(Yp=0.248±0.002), and resolves the cosmological constant and coincidence problems without fine-tuning. With only five free parameters (H0,Ωm,ns,As,ϵ)(H0,Ωm,ns,As,ϵ), the model yields χ2/dof=1.02±0.03χ2/dof=1.02±0.03, ΔAIC=42ΔAIC=42 relative to ΛCDMΛCDM, demonstrating strong statistical preference. EET-specific testable predictions include the transition redshift zt=0.5±0.05zt=0.5±0.05, hierarchical scaling M(L)∝L2.2±0.1M(L)∝L2.2±0.1, and the no-Big-Rip criterion. The framework unifies cosmic evolution with the same YEC grammar operating across scales, from quantum fluctuations to cognition, via the scaling law τ∝L0.6τ∝L0.6.