4.4 Comparison with FLRW and Gdel Universes
This framework bridges the gap between static rotating models (like Gdel) and homogeneous isotropic models (like FLRW) by proposing a dynamical, decaying rotational mode seeded by intrinsic spin. The result is a universe that starts with significant anisotropy and rotation but evolves naturally toward observational consistency---without requiring ad hoc inflationary mechanisms.
Summary
The analytical and numerical results demonstrate that incorporating torsion and spin in a Bianchi IX geometry offers a realistic and stable cosmological model. Early-universe rotation and shear---naturally sourced by spin density---can account for observational anomalies while preserving isotropy at late times. The system exhibits self-regulating attractor behavior, making it a compelling alternative or complement to CDM.
5. Observational Implications
The incorporation of rotation, torsion, and anisotropy in the early universe yields novel phenomenological consequences that can be tested against cosmological observations. In this section, we explore how the Einstein--Cartan--Bianchi IX cosmology impacts various cosmological probes and propose specific, testable predictions for upcoming surveys.
5.1 CMB Anisotropy Signatures and Alignment Effects
One of the key motivations for introducing cosmic rotation and torsion stems from the persistent anomalies in the low multipole moments of the Cosmic Microwave Background (CMB).
Multipole Alignment and the "Axis of Evil"
Planck and WMAP data have shown:
Dipole--quadrupole--octupole alignments (colloquially, the "Axis of Evil"),
