Non-Equilibrium Holographic Brane Cosmology in AdS5. II: Bulk Angular Momentum, Bianchi Type IX Regular Bounce, and CMB Parity-Odd Imprints

We extend the non-equilibrium holographic cosmological framework of Karch-Randall 3-branes embedded in an asymptotically Anti-de Sitter five-dimensional bulk (AdS5)—developed across Papers I-A through I-D—by relaxing the static spherical constraint and incorporating stationary bulk angular momentum (J_5 != 0). Modeling the exterior geometry of the collapsing five-dimensional progenitor via the exact equal-spin Kerr-AdS5 (Hawking-Hunter-Taylor-Robinson) black hole metric (a_1 = a_2 = a < L_5), the spatial isometry group is promoted from SO(3) to the cohomogeneity-1 group R x SU(2) x U(1). We prove that a radially moving 3-brane in this background acquires an exact, spatially homogeneous but anisotropic Bianchi Type IX cosmological metric endowed with spheroidal deformation (a_parallel != a_perp) and an off-diagonal inertial frame-dragging connection (dtau sigma_3).

Projecting the five-dimensional Riemann and Weyl curvature tensors via the Modified Shiromizu-Maeda-Sasaki (SMS) equations, we demonstrate that the diagonal electric Weyl dark radiation (-mu_5/R^4) remains invariant at leading order, while a chiral off-diagonal gravitomagnetic Weyl current E_03^(5) = (3 mu_5 a T') / (R^4 Xi) dynamically injects cosmic vorticity onto the brane while preserving the covariant Bianchi identity nabla^mu E_munu^(5) = 0. We establish a rigorous Quantum Dominance Theorem proving that the repulsive holonomy-corrected quadratic Israel stress (Pi_munu ~ -rho^2/rho_crit ~ -a^(-8)) asymptotically overwhelms the anisotropic shear kinetic density (sigma^2 ~ a^(-6)) by two powers of the scale factor, completely eliminating chaotic Kasner/Belinsky-Khalatnikov-Lifshitz (BKL) oscillatory singularities and enforcing a simultaneous, smooth quantum bounce (a''_perp > 0, a''_parallel > 0 at a_min).

During the subsequent inflationary phase, cosmic shear decays as Omega_sigma ~ e^(-6N) in accordance with the Wald no-hair theorem, whereas residual vorticity decays at the slower rate omega/H ~ e^(-2N). This differential damping hierarchy freezes a deterministic axial imprint across modes exiting the horizon during the first e-folds (k <= k_bounce), naturally resolving the CMB quadrupole-octopole alignment (ell = 2, 3, the "Axis of Evil"), satisfying Planck global vorticity bounds ((omega/H)_0 ~ 10^(-48) << 10^(-10)), and predicting a localized gravitational Faraday birefringence angle beta_rot ~ 0.2°–0.5° in odd-parity polarization spectra (C_ell^TB, C_ell^EB != 0 for ell <= 5).