How do We know that CMB is not moving itself, because the content of the universe was moving during decoupling?Dale said:They could compare each observer’s motion to the local inertial frame where the cosmic microwave background radiation is isotropic.
Because we arbitrarily choose the reference frame where it is isotropic. We do that because it makes the math easier and we arbitrarily prefer easy math over difficult math.exander said:How do We know that CMB is not moving itself, because the content of the universe was moving during decoupling?
Because seeing the CMB as isotropic is the meaning of "moving with space due to the expansion of the universe", which is what you asked about.exander said:How do We know that CMB is not moving itself
The basic point is that it is spacetime that underlies everything. There is no "space" or "time", just spacetime. If you want to talk about space or time separately you have to first slice 4d spacetime into a stack of 3d slices, each of which is "the universe at one time". But there isn't a unique way to do this. There are no gridlines built in to spacetime telling you how to slice (although there are limits about which direction you can sensibly call time).exander said:How can an observer distinguish two objects that are moving from each other in space compared to those that are moving with space due to expansion of the universe?
We know that the CMB has no net motion in space because we defined space to be the slicing of spacetime where the CMB has no net motion. It's true by definition.exander said:How do We know that CMB is not moving itself, because the content of the universe was moving during decoupling?
Claiming that CMB has not net motion is equivalent to say that spacetime's slicing it defines gives "space" slices that are all homogeneous and isotropic.Ibix said:We know that the CMB has no net motion in space because we defined space to be the slicing of spacetime where the CMB has no net motion. It's true by definition.
A non-tautological question would be: is the FLRW spacetime an accurate model of the real spacetime? Or, equivalently, are there observations which are inconsistent with us being in an FLRW spacetime (or at least one that looks FLRW on large scales)? The answer to those is a resounding maybe.
No. The Robertson-Walker spacetime is the most general spacetime satisfying spatial homogeneity and isotropy. It is basically just implementing those symmetries.cianfa72 said:Is possibile to conceive different spacetime models from FLRWs that are consistent with the homogeneity and isotropy features of CMB ?
Homogeneity no, not that I can think of. Isotropy is trivial; let the mass density vary with radial distance from the Earth. There are probably limits to how much variation you can have and be consistent with the observed existence of redshift of galaxies, and you probably get a complex relationship between redshift and intensity and time. It's also extremely contrived - of all thecianfa72 said:How the CMB is related to the FLRW spacetime models ? Is possibile to conceive different spacetime models from FLRWs that are consistent with the homogeneity and isotropy of CMB ?
Therefore CMB's both homogeneity and isotropic features in every point of the Universe force us to assume one of the 3 FLRW models (Spherical, Euclidean or Hyperbolic) ?Orodruin said:No. The Robertson-Walker spacetime is the most general spacetime satisfying spatial homogeneity and isotropy. It is basically just implementing those symmetries.
Then the model won't be homogeneous.Ibix said:Isotropy is trivial; let the mass density vary with radial distance from the Earth.
Sure - that's why I said I couldn't think of a homogenous model except for FLRW.PeterDonis said:Then the model won't be homogeneous.
I don't think we can conclude that the universe is homogeneous from the CMB alone. That only tells you that it's isotropic. You need to add the cosmological principle, or a study of other matter in the universe, or something of the sort to get homogeneity.cianfa72 said:Therefore CMB's both homogeneity and isotropic features in every point of the Universe force us to assume one of the 3 FLRW models (Spherical, Euclidean or Hyperbolic) ?
Yet, the only spacetime models that are both homogeneous and isotropic are the FLRWs models.Ibix said:I don't think we can conclude that the universe is homogeneous from the CMB alone. That only tells you that it's isotropic. You need to add the cosmological principle, or a study of other matter in the universe, or something of the sort to get homogeneity.
Yes. But the CMB is not the only piece of evidence supporting them.cianfa72 said:Yet, the only spacetime models that are both homogeneous and isotropic are the FLRWs models.
I see. I understood @cianfa72 to be asking if there were any other models that satisfied both properties, homogeneity and isotropy. If we only need to satisfy isotropy, then any spherically symmetric spacetime will do (for example, Schwarzschild).Ibix said:Sure - that's why I said I couldn't think of a homogenous model except for FLRW.
Depends how you read "consistent with the homogeneity and isotropy features of CMB". The CMB is isotropic, but without a few billion years' measurement I don't think we can say it's homogeneous with any confidence from CMB observation alone. Of course, we do have other lines of evidence pointing to homogeneity, like the large scale homogeneity of matter.PeterDonis said:I see. I understood @cianfa72 to be asking if there were any other models that satisfied both properties, homogeneity and isotropy.
Isotropy and a CMB. And we need to be at the middle, so it can't be pure Schwarzschild. That's actually why I was saying there were probably limits to the variation of density with radial distance that you can get away with. Presumably something that is not far from homogeneous would behave not that differently from an FLRW spacetime, would necessarily be isotropic to the special observer at the origin, but not be homogeneous.PeterDonis said:If we only need to satisfy isotropy, then any spherically symmetric spacetime will do (for example, Schwarzschild).
Sorry, when you talk of homogeneity and isotropy of spacetime you actually mean properties of the spacetime itself or properties of the spacelike hypersurfaces of specific foliations ?PeterDonis said:I see. I understood @cianfa72 to be asking if there were any other models that satisfied both properties, homogeneity and isotropy. If we only need to satisfy isotropy, then any spherically symmetric spacetime will do (for example, Schwarzschild).
When we say a spacetime is homogeneous and isotropic, what we mean is that there exists a foliation by spacelike hypersurfaces which have the required Killing vector fields.cianfa72 said:when you talk of homogeneity and isotropy of spacetime you actually mean properties of the spacetime itself or properties of the spacelike hypersurfaces of specific foliations ?
Ok, so assuming CMB isotropy does mean assuming isotropy (i.e. the existence of rotation KVFs about a point on foliation's spacelike hypersurfaces) at any point of any foliation's spacelike hypersurfaces ?PeterDonis said:When we say a spacetime is homogeneous and isotropic, what we mean is that there exists a foliation by spacelike hypersurfaces which have the required Killing vector fields.
Not necessarily, no. It is theoretically possible to have a model where the CMB is isotropic but something else is not.cianfa72 said:assuming CMB isotropy does mean assuming isotropy
Ok, claiming CMB is isotropic from measurement amounts to say it is isotropic just from the single point it is observed, I believe.PeterDonis said:Not necessarily, no. It is theoretically possible to have a model where the CMB is isotropic but something else is not.
Yes.cianfa72 said:claiming CMB is isotropic from measurement amounts to say it is isotropic just from the single point it is observed
Therefore we have not a direct evidence (by measurements) that CMB is actually isotropic w.r.t. other points in the Universe.cianfa72 said:Ok, claiming CMB is isotropic from measurement amounts to say it is isotropic just from the single point it is observed, I believe.
That's correct.cianfa72 said:we have not a direct evidence (by measurement) that CMB is actually isotropic w.r.t. other points in the Universe.
Well, the homogeneity of matter in the universe suggests that the universe is FLRW and hence the CMB is also homogeneous. But we haven't directly sampled the CMB elsewhere, no, due to not having been anywhere else.cianfa72 said:Therefore we have not a direct evidence (by measurements) that CMB is actually isotropic w.r.t. other points in the Universe.
But we don't actually know that by direct observation either. We assume it, and we have no observations so far that are inconsistent with that assumption (at least not when we specify that we only mean on large enough distance scales). But we have no direct confirmation of it either, for the same reason we have no direct confirmation of isotropy.Ibix said:the homogeneity of matter in the universe
Good point. I was thinking that we have a reasonable idea that the number density of galaxies is homogeneous, but really we only know its isotropic because we're seeing back into the past and the visible density does vary with distance. We attribute that to ##a## varying only with time, but the "only" is an assumption derived from the cosmological principle.PeterDonis said:But we don't actually know that by direct observation either. We assume it, and we have no observations so far that are inconsistent with that assumption (at least not when we specify that we only mean on large enough distance scales). But we have no direct confirmation of it either, for the same reason we have no direct confirmation of isotropy.
If the CMB is homogeneous everywhere and isotropic at a point then it is isotropic at any point (on foliation's spacelike hypersurfaces).Ibix said:Well, the homogeneity of matter in the universe suggests that the universe is FLRW and hence the CMB is also homogeneous.