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The cosmological principle states that the spatial distribution of matter in the universe is both homogenous and isotropic on a large scale. Isotropic means the universe looks approximately the same in all directions (when we observe the universe matter is not more prevalent in a specific direction, i.e. there are no special directions in the universe), and homogenous means one large region of the universe is approximately the same as any other large region of the universe (the average density of matter is approximately the same in any region of the universe, i.e. no special regions of the universe).
While there are local variations that exist, for example, some relatively small regions of space have more galaxies than others. The cosmological principle states that on average, over a large enough scale, you'll see the same number of galaxies, or matter, irrespective of where you look. The principle goes further to state any large region of the universe is effectively the same as another, containing the same number and same types of galaxies.
Diagram demonstrating the cosmological principle.
The cosmological principle is derived from the Copernican principle, but it does not have any foundation in any particular physical model or theory (i.e. it can not be proved in a mathematical sense). While the cosmological principle is supported by observations of the universe, it has also received criticism, with many arguing observations calling into question the universe's isotropy and homogeneity.
The Copernican Principle is a basic statement in physics that there should be no "special" observers. Before Copernicus, the Aristotelian model of the solar system placed the Earth at the center of the solar system, with everything revolving around it. Earth was believed to have a unique position. In the sixteenth century, Copernicus proved this model incorrect, with the Earth orbiting around the sun.
The Copernican principle is a cornerstone of astronomy and plays an important role in testing the viability of cosmological models. It is also a necessary consequence of the stronger assumption of the Cosmological Principle. If the Copernican principle states we do not live in a special part of the universe, the Cosmological principle goes further to state there are no special parts of the universe.
