On the cosmological principle Just more of a conceptual question on the mutual inclusivity of the cosmological principle. That is to say, I was wondering if it were possible to have a Universe that were isotropic but NOT homogeneous OR a Universe that were homogeneous but NOT isotropic. 

My spidey sense is telling me that it is possible that a Universe could be istropic but not homoegenous.

Surely, by default, if a Universe is homogenous then it follows that it has to be isotropic?
I was wondering if it were possible to have a Universe that were isotropic but NOT homogeneous OR a Universe that were homogeneous but NOT isotropic. 


Most people will be happy with the UC Berkeley definition that says homogeneous means "looks the same at every location" and isotropic means "looks the same in every direction". And some will know that as per Ned Wright's article, these attributes aren't quite the same: 

 

He says "the figure above shows a homogeneous but not isotropic pattern on the left and an isotropic but not homogeneous pattern on the right".  However as far as I know pictures like this just don't apply to our universe scattered with galaxies.  


  My spidey sense is telling me that it is possible that a Universe could be isotropic but not homogeneous.


My spidey sense is telling me some guy 46 billion light years away might say the universe is neither isotropic nor homogeneous. Because when he looks up, half the night sky is black or something. 


  Surely, by default, if a Universe is homogenous then it follows that it has to be isotropic? 


I agree with the gist of that. IMHO if an observer sees a homogeneous universe, he sees an isotropic universe too. Yes, one can find hypothetical scenarios wherein the universe is homogeneous but not isotropic. But they're only hypothetical. And let's not forget that it's only an assumption. If you lived in a forest would you assume that the world was covered in trees? Which look the same at every location and in every direction? It isn't a particularly scientific  assumption. For all you know some guy lives near the edge of the forest. I think you're better off saying we just don't know.