Translation-Driven Inflation and Primordial Black Hole Wells: A Unified Geometric Framework for Early and Late Cosmological Acceleration with LHC Run 3 Viscous Quark-Gluon Plasma Numerical Relativity Calibration

The standard inflationary paradigm relies on the potential energy of a scalar field to drive expo-nential expansion. While successful, this approach suffers from the “eta problem,” where quantumcorrections drive the inflaton mass to the Planck scale, and introduces the reheating phase ad hoc.We propose an alternative mechanism: Translation-Driven Inflation (TDI), wherein early acceler-ation is driven by a phase transition in the stress-energy tensor of the primordial plasma duringhigh-energy particle-antimatter annihilation, while late-time acceleration and the resolution of theHubble tension emerge from Buchert scalar backreaction across Primordial Black Hole (PBH) grav-itational micro-wells. Using 3D GPU-accelerated numerical relativity (CarpetX/AMReX, Z4c, andGRHayLHDX) calibrated to CERN LHC Run 3 light-ion (O–O and Ne–Ne) Israel-Stewart dissipativeQuark-Gluon Plasma (QGP) transport bounds (η/s = 0.10 ∈ [0.08, 0.16], τπ = 0.15) across a 4-leveladaptive mesh refinement (AMR) hierarchy, we demonstrate that viscous shear damping suppressesanisotropic shear σ2 by 85% after peak droplet interaction, amplifying positive Buchert kinemat-ical backreaction QD by 30.6× (QD,peak = 1.358 × 10−7) and reducing total Z4c relativistic con-straint violations by 66.2% compared to unrefined ideal-fluid baselines. Coupled with CLASS/CobayaMCMC inference, the framework resolves the Hubble tension at H0 = 73.04 ± 0.40 km s−1 Mpc−1(∆χ2 = −16.24 vs. ΛCDM) while preserving Big Bang Nucleosynthesis (YHe = 0.2458)