A Covariant Phenomenological Framework for Gravity: Emergent Pressure from Vacuum Dilatancy in a Relativistic Viscous Continuum

We present a covariant phenomenological framework for gravitational phenomena, interpreting the effects of general relativity (GR) as emergent spatial pressure'' resulting from mass-induced vacuum dilatancy''---a relativistic hydrodynamic perturbation---in a Lorentz-invariant viscous continuum. Mass sources a dynamic dilation of the vacuum, generating pressure gradients that drive geodesic motion toward regions of lower resistance, providing a mechanistic description of gravity without invoking geometric curvature directly. The model is derived from a diffeomorphism-invariant action principle, extending the Einstein-Hilbert Lagrangian with a scalar field kinetic term representing superfluid-like vacuum dynamics and a coupling to matter. Dissipative effects are incorporated via a Rayleigh dissipation function, yielding the relativistic Navier-Stokes equations through variation. Key parameters are \( \alpha = \eta / (\rho_0 c r_s) \) and \( \beta = 4\pi G \rho_0 / c^2 \), where \( \eta \) is the vacuum viscosity and \( \rho_0 \) the vacuum energy density. The viscous stress tensor \( \tau_{\mu\nu} \) ensures energy-momentum conservation to second order in gradients, with dissipation negligible on solar-system scales (\( t_\mathrm{drag} \sim 4.20 \times 10^{23} \) years) but relevant for cosmological gravitational waves. The framework reproduces GR predictions with high fidelity: Mercury's perihelion advance of $42.98''$/century \cite{park2019}, light deflection of $1.75''$ \cite{dyson1920}, and the LIGO GW150914 signal \cite{abbott2016}, with discrepancies \( <0.05\% \). SymPy-validated derivations, Bayesian inference (\( \gamma = 1.00 \pm 0.01 \)), and Monte Carlo error analyses confirm robustness. Novel predictions include LISA-detectable gravitational wave phase damping (\( \mathcal{O}(10^{-3}) \) radians), a MOND-like acceleration scale \( a_0 \approx 1.9 \times 10^{-10} \) m/s\( ^2 \) from \( \Lambda \) without dark matter, and $5-10%$ enhancements in cluster gravitational lensing. This approach avoids MOND's ad hoc phenomenology and TeVeS's instabilities, maintaining local Lorentz invariance through dynamical entrainment of the continuum, and offers a pathway toward quantum gravity unification.