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?

  • $\begingroup$ What dust do we see that is cosmological with local measurements? Do the same but observe what you can, stars, galaxies, and the CMB. They are not local. There is no local cosmological measurement you can do, it's all affected more strongly by local gravity (earth/sun, solar system, Galaxy, cluster) that the cosmological averages. $\endgroup$ – Bob Bee Nov 6 '16 at 7:54
  • $\begingroup$ I'm not talking about the actual universe, I'm talking about the FLRW solution. $\endgroup$ – AGML Nov 6 '16 at 15:57
  • $\begingroup$ Dust is not everywhere, it is a cosmological approximation. This is physics, not mathematical FLRW, it was never meant to be taken that rho (mostly dust density, ignoring dark energy) could be measured locally. Your question is a math question then. As such, mathematically yes. It means nothing. It's like other things young physics students get confused about: like, how can a force be non-conservative when all (ignore Einsteins gravity) elementary forces (EM, weak, strong, Newtonian gravity) are conservative? The answer is statistical mechanics and thermodynamics. Cosmological rho is not local $\endgroup$ – Bob Bee Nov 6 '16 at 19:06
  • $\begingroup$ How exactly do the local inhomogeneities prevent us from doing the above? Suppose we were inside a ~MPc sized spacecraft, if it makes you feel better. $\endgroup$ – AGML Nov 6 '16 at 19:25
  • $\begingroup$ It's like if I asked "does a simple harmonic oscillator oscillate periodically" and you responded "well no because real pendulums have friction". a) That is not the question I asked; and b) There are perfectly physical situations in which you can ignore the friction. $\endgroup$ – AGML Nov 6 '16 at 19:27

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