I'm utterly confused by co-moving distance, transverse comoving distance and proper distance. Is comoving distance = proper distance? Then what is transverse comoving distance? Here's what I know so far:(adsbygoogle = window.adsbygoogle || []).push({});

The FRW metric can either be expressed as

[tex]ds^2 = c^2dt^2 - a^2(t) \left[ \frac{dr^2}{1-kr^2} + r^2(d\theta^2 + sin^2 \theta d\phi^2) \right] [/tex]

or can be expressed as

[tex]ds^2 = c^2dt^2 - a^2(t) \left[ d\chi^2 + S^2(\chi) (d\theta^2 + sin^2 \theta d\phi^2) \right] [/tex]

Hobson describes: "##(\chi, \theta, \phi)## and ##(r,\theta,\phi)## are co-moving coordinates, where the galaxy has fixed coordinate positions were the 'cosmological fluid' is at rest. He also says that luminosity distance ##d_L = (1+z) R_0 S(\chi)## and angular diameter distance ##d_A = \frac{R_0 S(\chi)}{1+z}##.

My notes describe them as

To reconcile both material, it seems that proper motion distance is ##D_M = R_0 S(\chi)## and proper distance = ##D_C## which is path taken by light?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Comoving/Proper distance, transverse comoving distance

**Physics Forums | Science Articles, Homework Help, Discussion**