The Einstein--Cartan framework inherently bridges classical and quantum descriptions via spin--torsion coupling, offering a rich foundation for further theoretical exploration.
Loop Quantum Gravity (LQG) Compatibility:
Torsion appears naturally in the Ashtekar--Barbero variables and spin-network formulations,
Our macroscopic torsion field may be viewed as a semiclassical manifestation of quantum spin geometries,
Cosmic vorticity may arise from quantum coherence in early spin networks, potentially visible as entangled multipole modes in the CMB.
Spin Foam Cosmology:
The rotational degrees of freedom introduced here may correspond to nontrivial topological transition amplitudes in the spin foam path integral,
Torsion can act as a coarse-grained statistical variable encoding spin entanglement across quantum gravitational histories.
These links open possibilities to integrate our framework with non-perturbative approaches to quantum gravity, including causal dynamical triangulations, twistor-based cosmology, and group field theory.
7.4 Suggestions for Numerical Cosmological Simulations
While our analysis has been semi-analytical and conceptual, future work should incorporate full numerical simulation of the Einstein--Cartan--Bianchi IX dynamical system, including:
