What the CMB sky looks like in a universe that isn't the same in all directions

Growing tensions in cosmological data — from supernova surveys to bulk-flow measurements — have raised questions about when and whether the universe truly looks the same in every direction. Starting from spatially homogeneous but anisotropic Bianchi models, the authors construct metrics, derive Newtonian-gauge perturbation equations analogous to the standard FLRW treatment, and reduce them to a single characteristic PDE. Applying this to a Bianchi V toy model, they simulate the resulting CMB anisotropy power spectrum, offering a concrete template for what directional asymmetry would imprint on the microwave sky.