Cosmological Principle

We do not occupy a preferred place in the Universe (Copernican belief) and further, that at a given time, the Universe appears homogeneous and isotropic to all observers

Homogeneity and Isotropy of the Universe

The question of the homogeneity and isotropy of the Universe cannot be answered until one specifies the size of the region which should be averaged over. For example, the Solar System is clearly inhomogeneous; there is a star at the center of the system which is surrounded by objects. The Solar System looks differently depending upon where you look. The scale upon which the Universe should appear homogeneous and isotropic is not well-defined, outside of the requirement that it is large.

The homogeneous and isotropic assumptions are tough. Recall that the CMBR is homogeneous and isotropic but that regions in the Universe which are in opposite directions are not causally connected and so really have no reason why they should have the same properties. Why?

This is known as the Horizon Problem