Phenomenology of Rheological Gravity: A Finsler-Randers Geometric Extension for Spacetime Dynamics

The current cosmological paradigm relies on static dark matter halos to effectively describe galactic dynamics and structure formation. In this work, we propose a geometric alternative based on Rheological Gravity, wherein spacetime is modeled as a multifractal network exhibiting fluid-like viscoelastic properties. Utilizing a Finsler-Randers geometric extension, we formalize a "yield limit" (a0) and an elastic relaxation time (τR). We introduce a dimensional phase transition where the fundamental Hausdorff dimension of the vacuum sublimates to dH ≈ 2 in the weak acceleration regime. Furthermore, governed by the Deborah number, we demonstrate that the effective metric relaxation time is dynamically bounded by the Hubble cosmic strain rate (H0) and local kinematic shear (ωₗocal), naturally deriving the MOND empirical scale. This framework predicts that moving baryonic masses generate a directional asymmetry in the local vacuum topology: a metric compression in the leading vector (bow) and a metric hysteresis in the trailing vector (wake). This phenomenon offers a geometric resolution to the anomalous offset in merging systems like the Bullet Cluster via "topological inertia". To empirically test this theoretical asymmetry, we propose the Janus Project, implementing a kinematic stacking pipeline using galaxy-galaxy lensing data from surveys like the Sloan Digital Sky Survey (SDSS). Future high-precision weak lensing surveys will be instrumental in differentiating this geometric metric wake from conventional dynamical friction effects, offering a novel perspective on the fluid dynamics of spacetime.