Dead Universe Theory: A Parameter-Free Eigenvalue of the Cosmological Growth Sector and the Resolution of the Hubble and S₈ Tensions

The Dead Universe Theory (DUT) proposes that observed cosmic dynamics arise not from primordial singularity and metric expansion, but from asymmetric thermodynamic retraction within a viscoelastic spacetime continuum — the relic geometry of a prior cosmological phase. This work presents the complete mathematical formulation of DUT, grounded in an extended variational action from which the entropic deformation tensor Ξμν emerges via metric variation, establishing the field equations as a natural dissipative extension of General Relativity.DUT introduces two distinct dimensionless indices governing separate physical sectors. The first, γ = (√5−1)/2 ≈ 0.6180339887, is the effective growth index of the linear structure-growth sector, derived as the unique physical root of the characteristic equation γ² + γ − 1 = 0. This value emerges from the asymptotic closure of the reduced perturbation system under thermodynamic constraints, confirmed independently by four convergent arguments: variational origin of Ξμν, dynamical attractor stability, retraction duality symmetry γ ↔ 1−γ, and the Bianchi identity constraint Γ = 3(1−γ). It is not a fitted parameter — it is fixed before any data is consulted. The second, η ≈ 0.958, is the background entropic-response parameter controlling the proximity of the DUT expansion history to ΛCDM. In the limit η → 1, entropic corrections vanish identically and standard Friedmann dynamics are recovered, explaining why BAO and Type Ia supernovae measurements remain observationally consistent with ΛCDM within current precision.This two-sector structure resolves simultaneously the two most persistent tensions in precision cosmology. The Hubble tension — the >5σ discrepancy between CMB-inferred H₀ ≈ 67.4 km/s/Mpc and locally measured H₀ ≈ 73.0 km/s/Mpc — is addressed by the DUT background solution, which yields H₀ ≈ 73.88 km/s/Mpc without introducing additional free parameters. The growth tension (S₈ discrepancy) is resolved through the fixed growth index γ ≈ 0.618 > 0.55, which produces a systematic suppression of late-time structure growth relative to ΛCDM predictions, precisely in the direction indicated by weak lensing surveys. When evaluated against a compilation of 37 independent RSD measurements of the growth rate fσ₈, the DUT prediction yields χ²_DUT = 25.58 (χ²_red ≈ 0.69), compared to χ²_ΛCDM = 66.67 for the same dataset, corresponding to Δχ² = −41.09 and a relative reduction of 69.85% — with zero free parameters in the growth sector.The theory is decisively falsifiable. If future measurements establish γ outside 0.618 ± 0.03, DUT is refuted without recourse to parameter adjustment. The Euclid mission, with target precision Δγ ~ 0.01–0.02 at 1σ, will test the predicted separation Δγ ≈ 0.068 relative to ΛCDM at 3–4σ significance. All equations and numerical predictions are fully reproducible via three publicly available computational pipelines, including the TON618 v1.1 Unified Bayesian Cosmology Engine and the DUT-CMB Scientific Engine 3.0.Keywords: Dead Universe Theory, thermodynamic retraction, growth index, golden ratio, viscoelastic spacetime, Hubble tension, S₈ tension, structure formation, entropic deformation tensor, falsifiable cosmology