A Unified Rank-2 Tensor Paradigm for Cosmic Inflaton Decay:\\ Resolving the H₀ and S₈ Anomalies via Causal Viscous Hydrodynamics

We present a novel, first-principles cosmological framework that unifies inflation, dark matter, and dark energy under a single primordial rank-2 tensor field Bμν. Following the cessation of inflation, a scale-separated decomposition splits the field into a frozen, long-wavelength background baseline (Bμν(S)) driving dynamic, late-time cosmic acceleration, and a rapidly oscillating subhorizon mode (Bμν(F)) that behaves macroscopically as cold dark matter. During the reheating epoch, explosive particle production via broad parametric resonance pumps energy density into the fast-oscillating sector; concurrently, this non-equilibrium injection introduces an inherent macroscopic fluid dissipation, establishing a microphysical origin for cosmic friction. By varying the ghost-free bimetric action, we derive the closed and modified Einstein Field Equation: Gμν=8π G [Tμν(S)+Tμν(F)+Π(gμν+uμuν)], where the dynamic bulk viscous pressure Π is governed by a causal, non-linear Israel-Stewart transport equation explicitly dependent on the changing global expansion rate: Π̇ = -Π/τ₀ - 3Hζ/τ₀ - 1/2Π ( 3H - ρ̇FρF + ḢH ). Numerical integration of this autonomous system reveals a stable thermodynamic attractor tracking from Π(z=10) = -258.17 down to a dark-energy-like de Sitter floor of Π(z=0) = -3.18. This dynamic evolution smoothly increases the local Hubble expansion rate to resolve the H₀ tension, while the active early-universe viscous stress introduces a scale-dependent braking term (∝ k²) that exponentially dampens the small-scale matter power spectrum $P(k)$, eliminating the S₈ over-clustering discrepancy. Finally, we establish precise observational benchmarks and falsifiability criteria for this model, detailing how its signature Gaussian-type power cutoff can be unambiguously detected through tomographic weak lensing by the Euclid Satellite and the Vera C. Rubin Observatory (LSST), mass-function limits on satellite dwarf galaxies by the Nancy Grace Roman Space Telescope, and high-redshift 21cm intensity mapping by the Square Kilometre Array (SKA).