The Cosmological Principle
Universe highly isotropic
- CMBR anisotropy _ O(10–5)
Unless we occupy the “center of the Universe,” it must also be homogenous
_ maximally symmetric space
- Flat Euclidean space R3
- Closed three-sphere S3=SO(4)/SO(3)
- Open three-hyperbola SO(3,1)/SO(3)