Viscoelastic General Relativity (VGR): A Screenless Geometric Framework for Cosmic Gravitational Anomalies

This paper introduces Viscoelastic General Relativity (VGR), a novel, action-based extension of Symmetric Teleparallel Gravity (f(Q)) that provides a closed geometric alternative to non-baryonic dark matter. Unlike previous modified gravity models that rely on "Chameleon" screening or ad-hoc density filters to pass solar system tests, VGR utilizes the External Field Effect (EFE). By defining vacuum memory activation as a function of the total environmental gravitational gradient (|∇Φ_Total|), the theory naturally recovers General Relativity in dense regions like the Solar System while activating modified dynamics in the sparse galactic outskirts. Key Contributions: • Ghost-Free Stability: Formulated as a strictly second-order, diffeomorphism-invariant theory, bypassing Ostrogradsky instabilities. • Unified Memory Mechanics: Introduces a Spacetime Memory Scalar Field (ψ) that accounts for the "missing mass" observed in galactic rotation curves via a fixed cosmic viscosity threshold (a_*). • Dissociative Merger Resolution: Resolves the "Bullet Cluster" paradox through a causal metric transport lag (τ_sky ≈ 0.121 Gyr), explaining gravitational lensing potential overshoots without collisionless particles. • Empirical Validation: Demonstrated via a χ²_ν ≈ 1.04 fit across a master database of ten galaxy cluster mergers and the SPARC galactic rotation catalog.