I had an interesting chat the other day about what sort of information an arbitrary observer needs to recover the comoving time in the FLRW universe.
Suppose one performs the following procedure:
-Look out at the surrounding dust. It is, for general observers, relativistically beamed and thus anisotropic.
-Map the anisotropic dust field to an isotropic one. Correct the observed redshift distribution to be isotropic as well. This should allow you to measure your speed relative to the expansion at any given moment.
-Measure the Hubble constant as a function of your proper time from the "corrected" isotropic dust. Since we also know our speed, we can recover the map from proper to comoving time as well.
Therefore, in the approximation that Universe is exactly FLRW, the comoving frame appears to be accessible to all observers from local measurements. Of course this is equally true of any frame, but it's still kind of interesting. Would this procedure work?