Author Topic: Different geometries  (Read 98 times)

cheetos

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Different geometries
« 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.

oelgaroy

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Re: Different geometries
« Reply #1 on: 15. January 2021, 15:32:50 »
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.

cheetos

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Re: Different geometries
« Reply #2 on: 15. January 2021, 16:33:30 »
Thanks for the answer! What course has the mathematical proof? I might look into it to see if I understand :)

oelgaroy

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Re: Different geometries
« Reply #3 on: 15. January 2021, 16:56:31 »
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