The FLRW metric is often described using the symbol \(\chi\). It occurred to me that many of our viewers would not recognize this angle. The metric can be expressed as a 3d hypersphere for its spatial part

\[dl^2=R^2(d\chi^2+sin^2\chi d\phi^2\]

the 3d hyper sphere is an embedding in 4d space using (x,y,z,w) in the following manner below

 

 

For some reason trying to insert images messes up latex instructions in the above but in this case its still readable.

anyways the above is from the following reference 

https://jila.colorado.edu/~ajsh/astr3740_14/flrw.pdf

see section 10.1

I am considering adding this diagram to the pinned threads above for easy reference. Thoughts ?

Edited August 18, 20241 yr by Mordred

As no one expresses an interest in having this diagram in one of the locked threads above. I will let the proposal go.