Dead Universe Theory (DUT):A Complete Formulation of Thermodynamic Retractionand the Universal Growth Index γ = (√5 − 1)/2

The Dead Universe Theory (DUT) proposes a fundamental re-examination of cosmic dynamics, replacing the standard paradigm of an expanding universe from a hot singularity with a model of asymmetric thermodynamic retraction within a viscoelastic spacetime continuum. In this framework, the observable cosmos constitutes a localized photonic anomaly — a transient luminous fluctuation — embedded within the collapsed gravitational geometry of a prior cosmological phase. This work presents the complete mathematical foundation of DUT, deriving the entropic deformation tensor Ξ_μν from a variational principle and incorporating it into modified Einstein field equations. The central result is the emergence of a unique, non-adjustable growth index γ = (√5 − 1)/2 ≈ 0.6180339887, derived as the asymptotic attractor of the perturbation dynamics rather than as a free parameter fitted to observational data. This value — the golden ratio — arises directly from the characteristic equation governing irreversible thermodynamic asymmetry. We present a complete, gap-free derivation of this result in Appendix A, where the golden ratio emerges as the unique fixed point of the scale-invariant dissipation/organization partition of the viscoelastic vacuum — a geometric consequence requiring no phenomenological ansatz or external prescription. The theory yields additional testable predictions including a mildly negative curvature parameter Ω_K ≈ −0.07 ± 0.02, a cosmic energy exhaustion timescale of approximately 166 Gyr, and specific signatures in high-redshift galaxy populations consistent with JWST deep-field results. Decisive falsification tests are provided for the Euclid and Roman Space Telescopes.