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Cosmologists say that the universe is homogeneous and isotropic within our Hubble volume based upon the astronomical observations. But how can we argue that the universe is homogeneous and isotropic at any particular moment while we can't picture the entire universe simultaneously due to the finite speed of light? i.e. when we picture the universe we picture the past. The further we go the further in time we observe.

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  • $\begingroup$ Are you talking here of a space or time related isotropy? $\endgroup$
    – dan
    Feb 3, 2016 at 17:40
  • $\begingroup$ The universe is "spatially" homogeneous and isotropic. So actually I mean space. $\endgroup$
    – maha
    Feb 3, 2016 at 18:04

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I think there are two ways to approach the question.

If you are coming from the point of view of a theoretician trying to come up with a working model of the universe, you would definitely like to make the assumption of isotropy and homogeneity. This is usually what we do, as least to first order approximation. One of the reasons for that is that the symmetry allows us to write useful and relatively simple solutions to Einstein's equations, like the FRW metric. Motivated by the fact that the universe is definitely not homogeneous at very small scales (read, scale of several galaxies), Cosmologists then add perturbations to this homogeneous and isotropic background, and see what they can get.

The second, more pragmatic approach is to look at the stars and see if the universe is homogeneous and isotropic. In other words, are the assumptions I discussed above justified. It turns out that they are. You were asking more specifically about the Hubble Radius, but it is not very much different from the observable universe. To sum up, we don't know for sure that the universe doesn't have a big "lump" just out of reach of what we can see today, but given what we can see and the fact that we have extremely accurate and predictive models of the universe that crucially rely on the basic assumptions of isotropy and homogeneity, it's a very justifiable thing to say.

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  • $\begingroup$ exhaustives measures taken by wmap and planck agree with both principles $\endgroup$
    – user46925
    Feb 3, 2016 at 16:39
  • $\begingroup$ I want to speak pragmatically. Actually the universe is observed to be homogeneous and isotropic on large scales but here comes my question, we actually look at the past! $\endgroup$
    – maha
    Feb 3, 2016 at 16:40
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    $\begingroup$ I'm not sure what your question is here. Do you mean that what we observe is the "past", therefore how do we know that the universe is homogeneous and isotropic in the "present"? Something along those lines? $\endgroup$
    – pploops
    Feb 3, 2016 at 16:47
  • $\begingroup$ Yeah exactly, I'm confused! $\endgroup$
    – maha
    Feb 3, 2016 at 16:50
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    $\begingroup$ @daniel Azuelos: You correctly understood that what we're comparing is the density of matter distribution from our point of view. But that's just the thing, our point of view is the only thing that makes physical sense to talk about. The notion that what we see doesn't exist any more is wrong: If you were to travel to these places at the speed of light, starting today, you would literally be travelling to the future. In other words, the best notion of "now" that we have for galaxies that we observe billions of light year away, is only what we see today. $\endgroup$
    – pploops
    Feb 3, 2016 at 21:25

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