Why Cosmic Acceleration is Rotational, Not Radial: Resolving the Friedmann Big Bang Instability

This work resolves the Copernican violation and the naked singularity catastrophe of recent one-dimensional radial models by elevating the Einstein–Euler Big Bang instability into a fully three-dimensional, rotational, and solenoidal continuum: Restoration of the Copernican Principle: In contrast to one-dimensional radial shock models that require an observer to sit near the center of an inhomogeneous spherical wave, unstable modes in three dimensions excite an isotropic, space-filling cascade of gravito-magnetic field sheets. The release of geometric field tension across localized topological reconnections drives cosmic acceleration uniformly in all directions, eliminating the need for a privileged center or dark energy. Vorticity–Curvature Equivalence: Formulating the continuum through the Gordon optical metric proves that fluid vorticity is physically identical to spacetime gravito-magnetic curvature. This restores the vortex stretching tensor and active enstrophy cascade that are artificially eliminated in irrotational radial flows. Curvature Regularization at the Big Bang: The singular backward-time collapse of the Friedmann saddle point is halted by an autonomous core cutoff bounded by causal velocity limits and turbulent dissipation. This caps the maximum Kretschmann curvature scalar to a strictly finite bound, replacing the unregularized naked singularity with a smooth bifurcation of hyperbolic null points. Observational Test: The isotropic dissipation of gravito-magnetic tension generates a distinctive negative third-order cubic coefficient in the expansion of luminosity distance with redshift. This negative shift cleanly separates three-dimensional gravito-magnetic turbulent relaxation from the positive signature of one-dimensional radial shocks while matching high-redshift supernova and baryon acoustic oscillation surveys.