This question is an upshot of a previous question asked by me.

The FRW metric of the Universe is based on homogeneity and isotropy of the universe on a length scale of 100 Mpc or larger. If we go back in time, do we expect the assumption of homogeneity and isotropy to be valid on even smaller and smaller length scales (i.e., the assumption expected to become better) or even larger and larger scales (i.e., the assumption expected to become poorer)?

I guess the assumption must become better because it is assumed to be valid close to inflation when the universe was tiny. But I'm not sure and cannot convince myself.

  • $\begingroup$ A very interesting question. My gut feeling is also that the assumption is valid on smaller and smaller scales. I may come back to you with an answer tomorrow! :) $\endgroup$
    – astronat
    Aug 2 '17 at 23:02
  • $\begingroup$ @astronat You may also find the post physics.stackexchange.com/questions/499259/… to be related. $\endgroup$
    – SRS
    Aug 30 '19 at 4:55

You assume the universe is isotropic and homogeneous through time as a whole, this is unchanging. The assumption is equally valid through time also, as all that is changing is the spacing between all matter, at an equal rate. You have to bear in mind this is an assumption made to help with ease of calculations, and isn't strictly speaking the case.

That said, there is some interesting reading about how the universe had to be slightly non-uniform at its beginning for planets, stars, solar systems etc all to form.

  • $\begingroup$ "You assume the universe is isotropic and homogeneous through time as a whole, this is unchanging." The question is why would you assume this and at what level of approximation? Any assumption must have some rationale. It's not that we assume so because if we assume homogeneity and isotropy it simplifies Einstein's equations. @G.Bruce $\endgroup$
    – SRS
    Aug 2 '17 at 13:30
  • $\begingroup$ It all depends on what scale you consider. On scales smaller than a few hundred million light-years, you can have some pretty significant inhomogeneties. But observations show that the universe is homogeneous on scales larger than that. That is, compare any two slices of the sky that are a few hundred million light-years across, and they'll look pretty much the same. It makes large scale calculation easier, when looking at the universe as a whole, much less when performing calculations about specific regions $\endgroup$
    – G.Bruce
    Aug 2 '17 at 13:42
  • $\begingroup$ The question asks something else and you're answering something else already I know. $\endgroup$
    – SRS
    Aug 2 '17 at 14:26
  • $\begingroup$ The universe large enough to on a whole be considered homogeneous and isotropic almost immediately. Unless your calculations are concerning the moment of creation, time is not a factor. My comment was meant to clarify that while the universe as a whole is considered unchanging (while expanding), you cannot consider it to be homogeneous and isotropic on any level of approximation $\endgroup$
    – G.Bruce
    Aug 2 '17 at 14:31
  • $\begingroup$ The universe has been expanding uniformly, so the assumption of an isotropic and homogeneous system is equally valid now as it was when the universe was much smaller $\endgroup$
    – G.Bruce
    Aug 2 '17 at 14:36

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