Can exotic cosmic geometries explain CMB's large-scale anomalies?

Working within the eight geometries of Thurston's geometrization conjecture, the authors derive transfer equations for CMB temperature and polarization in each anisotropic spacetime and track how signals evolve over time via Stokes parameters. The goal is to find patterns that could distinguish one geometry from another — and from the standard isotropic model — using quadrupole-scale CMB data. Results show that spatial curvature and underlying symmetry leave characteristic imprints on Q, U, and V polarization amplitudes. The work provides a concrete framework for confronting exotic cosmic topologies with precision CMB observations.