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AST 3220 => Questions about the lectures and the lecture notes => Topic started by: cheetos on 15. January 2021, 14:42:39

Hi, I don't know if I'm missing something. But do we have any explanation on why/how the spherical and hyperbolical geometries follow the CP? Or is maybe the answer to that in other courses? I want to try to understand rather than just accept the choice of geometry.

I haven' provided any proof, but in the case of positive curvature I pointed to the two dimensional case, where the surface of a sphere seems to be obviously homogeneous and isotropic. For the hyperbolic case I just stated that it is so. There is a mathematical proof for the RW line element with k=1,0,1 representing all possible geometries satisfying the cosmological principle, but we will not go into that in this course.

Thanks for the answer! What course has the mathematical proof? I might look into it to see if I understand :)

I am not sure, but maybe they prove it in the general relativity course in the Physics department. You can also try to read Robertson's paper, found here:
https://www.jstor.org/stable/85282?seq=1#metadata_info_tab_contents