Testing the Copernican and Cosmological Principles in the local universe with galaxy surveys

Understand

Cosmological density fields are assumed to be translational and rotational invariant, avoiding any special point or direction, thus satisfying the Copernican Principle.

• A spatially inhomogeneous matter distribution can be compatible with the Copernican Principle but not with the stronger version of it, the Cosmological Principle which requires the additional hypothesis of spatial homogeneity.
• We establish criteria for testing that a given density field, in a finite sample at low redshifts, is statistically and/or spatially homogeneous.
• The basic question to be considered is whether a distribution is, at different spatial scales, self-averaging.