homogeneous and anisotropic cosmology

Can a cosmological model homogeneous but anisotropic? What would that construction imply? are there observable consequences, and which ones would that be? (question courtesy of R. Schmidt, Centre for Astronomy, Heidelberg)

bonus question: What’s the angle between an edge and the space diagonal in an \(n\)-dimensional unit hypercube? What’s the limit of this angle in the case \(n\rightarrow\infty\)?