The assumption that, on the large scale, the universe at any given time is the same everywhere-isotropic and homogeneous.
The postulate, put forth by most cosmologists, that the universe is both homogeneous and isotropic; it is sometimes stated that the universe looks the same to all observers everywhere.
assumption that the Universe-at-large looks the same to all observers.
an assumption that the universe is everywhere uniform and looks the same in any direction---it is homogeneous and isotropic.
The idea that all observers, everywhere in space, perceive the Universe in roughly the same way regardless of their actual location.
The assumption that any observer in any galaxy sees the same general features of the universe.
The Cosmological Principle is not a principle, but rather an assumption or axiom that, when applied, severely restricts the large variety of possible cosmological theories.