Reproduce realistic anisotropies,
Compare with CMB multipole moments,
Estimate the contribution of torsion to the Hubble constant.
Summary
The field equations derived here represent a physically motivated extension of general relativity that incorporates spin and torsion within a rotating, anisotropic universe. The resulting dynamical system governs the evolution of expansion, shear, and vorticity, offering a natural explanation for observed anomalies and a pathway to resolve outstanding cosmological tensions.
4. Analytical and Numerical Analysis
This section investigates the dynamical evolution of rotating hyperspherical universes with torsion by applying analytical techniques and numerical simulations. We explore how the inclusion of intrinsic spin and anisotropic expansion influences the behavior of rotational modes, the curvature of space, and the stability of the cosmological model. These analyses are framed within the Einstein--Cartan--Bianchi IX formalism established in Section 3.
4.1 Initial Conditions and Parameter Space
We consider a homogeneous, anisotropic universe described by the Bianchi type IX metric with initial data set at the Planck epoch or slightly thereafter. The key dynamical variables are:
