Is there any evidence against the Cosmological Principle? I have been slowly getting more into math, but haven't gone into differential geometry or anything like that yet, so this question might be basic. Trying to get a deeper understanding of the Cosmological Principle, and why we assume it without question.
Physics/cosmology books make the assumption that the universe is isotropic, because (to summarize), "every observation we have made with telescopes show that the universe looks the same in all directions".

Because of that assumption, and the second assumption that the Earth/Sun aren't the center of the universe (the Copernican Principle), we make a final assumption that the universe must be homogeneous. Together creating the Cosmological Principle.
Has there been any evidence that these assumptions could be invalid? In terms of isotropy, do our observations that "the universe looks pretty much the same no matter where you look with a telescope" agree with a mathematical definition of isotropy? (Not sure what that, haven't dug much into algebraic/differential geometry yet). If it doesn't match exactly, what are some of the edge cases?
 A: As we moved from Geo-centric and Helios-centric models of the universe, natural philosophers began the trend of viewing the universe as 'less anthropic'.  That is to say, our existence and perception do not impose significant 'weight' or 'influence' upon the casual billiards of heavenly bodies.  The evolution of the cosmos occurs irrespective of the presence of life
Also the universe, as far is observation yields is not 'exactly' homogeneous.  We say it's isomorphic because the alternative idea, that of light and electricity existing as waves upon some 'Ether' was disproved by the observation that light does not change speed depending on what direction we are looking.  All I know of differentiable geometry, is it is fancy a process of measuring volumes and densities within a 'reasonable' degree of accuracy.  We say cosmos is isomorphic because the proportion of and effects of gravity upon matter appear to be consistent from galaxy to galaxy, cluster to cluster, and conferrers no polar or directional bias.  We say it is homogeneous because material appears fairly evenly spread in any direction.  How ever this falls apart if we to model a cubic meter of matter/energy upon the surface of the sun vs a cubic meter within the Oort. Galaxies are themselves aggregates of energy density, and tend to occur in clusters and so we take a wide enough cubic volume, average to a specific degree of precession our measurement of energy density within, and viola!  Homogeneous!  I assure you this is all the evidence we need and it is very scientific!
The the principle your referring to is more of a feel-good statement us atheists use to re-assurance ourselves that existence isn't some bizarre meta-stable fluke about to topple into entropic void.  Everything appears to be functioning, for lack of a better term, nominally.  Carry on!
