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We know that the CMB is isotropic when viewed outside of the spinning and revolving earth.

Is it homogeneous?

Can we relate the CMB to an inertial frame in the Newtonian sense (in which space and time are homogeneous and isotropic)? Or can it just provide an idea to build upon a new theory in which global (privileged) inertial frames exist?

Einstein's General Theory of Relativity could be useful in an answer, but some outside-the-box thinking would be appreciated; feel free to question GR.

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    $\begingroup$ Well, actually the CMB is not completely isotropic, even from the point of view of the solar system's barycenter. It has a dipolar component which can be interpreted as the motion of the solar system relative to it, and also some small fluctuations. $\endgroup$
    – Edgar Bonet
    Commented Jul 4, 2011 at 12:40
  • $\begingroup$ @Lakshya I see that you are still a beginning student, and maybe this link will help you get the data on CMB which has a map of the inhomogeneities. en.wikipedia.org/wiki/CMB . $\endgroup$
    – anna v
    Commented Jul 4, 2011 at 15:49
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    $\begingroup$ @Lakshya I need time to make a compreensive answer. The Einstein Relativity is not enough to deal with this problem. In SR the point of view is from a mobile observer taking in account that the two-way speed of light is c0, and constant as it is. I will not say against Einstein. I will have to go beyond we can find in the books to make clear the properties of the CMB referential. In the meantime you can have a look to the online book of Hans de Vries and also here. $\endgroup$
    – Helder Velez
    Commented Jul 5, 2011 at 17:17
  • $\begingroup$ @HelderVelez: Since you've collaborated with Oliveira (the author of the second link you gave), you should disclose that. Oliveira is a crackpot. We've discussed your work with Oliveira previously on physics.SE: physics.stackexchange.com/a/13348/4552 $\endgroup$
    – user4552
    Commented Jun 19, 2013 at 3:06

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This is a good question, unfortunately my answer will not be adequate.

The CMB does define a special frame of reference, atleast if one ignores fluctuations, there is a special frame where the CMB spectrum is homogeneous and isotropic. However it will not be in contradiction with the theory of relativity.

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  • $\begingroup$ I think we can approximate the CMB's homogeneity and isotropism, for the intents and purposes of moving around inside a solar system or even inside our own galaxy. The CMB is just so unimaginably far away that any errors that we might get are going to be incredibly minuscule as long as we stay inside our own galaxy...? Maybe! $\endgroup$
    – Nuke
    Commented Sep 9, 2022 at 9:32
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We know that the CMB is isotropic when viewed outside of the spinning and revolving earth.

As pointed out in Edgar Bonet's comment, this isn't true.

Is it homogeneous?

Realistic cosmological models describe it as approximately, but not exactly, homogeneous. Homogeneity and isotropy can't be perfect, since the universe does have structure.

Can we relate the CMB to an inertial frame in the Newtonian sense (in which space and time are homogeneous and isotropic)?

You're mixing up a lot of unrelated ideas here. Inertial frames in GR are local, and spacetime is locally homogeneous and isotropic in any such frame. At any point in spacetime, the CMB can be used to define an inertial frame. Spacetime is locally homogeneous and isotropic in that frame. Spacetime is also locally homogeneous and isotropic in every other inertial frame, including frames in which the CMB is not isotropic. Anisotropy of the stuff that occupies space doesn't imply anisotropy of space itself.

Or can it just provide an idea to build upon a new theory in which global (privileged) inertial frames exist?

No, you can't have global inertial frames (because an inertial frame is a free-falling frame, and, e.g., a free-falling frame in China doesn't correspond to a free-falling frame in America). No, it doesn't have anything to do with a privileged frame, because the existence of some stuff occupying space doesn't imply a privileged frame. A privileged frame would be one in which the form of the laws of physics was different. No, it doesn't imply the need for a new theory.

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