Viscoelastic Spacetime Dynamics and Galactic Rotation: A Comparative Analysis of "The Geometric Thaw" Framework and Standard ΛCDM

The ΛCDM paradigm models galactic rotation curves via collisionless particulate dark matter halos, yet it faces persistent structural failures, most notably the “cusp-core” discrep ancy in dwarf galaxies. This paper tests an alternative continuous-media framework, “The Geometric Thaw,” which reinterprets dark matter phenomenologies as the macroscopic vis coelastic frame dragging of a 14-dimensional spacetime manifold. Treating the vacuum as an Oldroyd-B viscoelastic fluid, we derive a two-parameter kinematic equation dependent on Geometric Stiffness (k) and a Viscoelastic Relaxation Length (λ). Using Markov Chain Monte Carlo (MCMC) regression, we evaluate this model against the standard Navarro Frenk-White (NFW) profile utilizing strictly filtered, high-fidelity kinematic and 3.6 µm photometric data from 175 galaxies in the SPARC database. Point-by-point deconstructions of representative morphologies—NGC 5055 (massive HSB), UGC 06614 (giant LSB), and IC 2574 (gas-dominated dwarf)—demonstrate that the viscoelastic formulation natively reproduces linear inner cores, extended flat profiles, and declining outer edges without ad hoc baryonic feedback tuning. The viscoelastic manifold achieves a vastly superior global Reduced Chi-Square (χ2 ν) and Bayesian Information Criterion (BIC) score, suggesting that supplementary galactic rotation velocities are the direct dynamic geometric response of the vacuum to baryonic shear stress.

Keywords: Dark Matter, Galactic Kinematics, SPARC Database, Viscoelasticity, NFW Profile, Modified Gravity