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I have read that the measurements of the cosmic microwave background indicate that the Universe has a flat geometry on large scales. Could one assume then that the Universe is acceleratingly rotating around some axis and that the centrifugal force of this rotation produces Universe's accelerated expansion and could this suggestion possibly eliminate the need for introducing the concept of dark energy, which was suggested/hypothesized mostly to accommodate/explain accelerated Universe expansion, observable by spectral red shift of far away Galaxies.

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I'm not sure how universal rotation is supposed to produce dark-energy-like effects in your scenario, but if there was a rotational effect, it would operate perpendicular to the axis of rotation but not parallel to it. This would produce a clear anisotropy in the expansion of the universe, which we simply don't see.

In fact, Stephen Hawking pointed out back in 1969 that rotation of the (visible) universe would produce a detectable signature in the cosmic background radiation; the absence of any such signature put upper limits on any possible rotation. Subsequent studies have only strengthened this; a paper by Saadeh et al. in 2016 puts limits that are about $10^{8}$ times more stringent than Hawking's original paper.

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  • $\begingroup$ What were the constraints provided in Hawking's original paper? $\endgroup$ Jul 19 at 19:19
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    $\begingroup$ $\omega / H_{0} < 10^{-3}$, where $\omega$ is the vorticity (twice the angular velocity for a uniformly rotating system). $\endgroup$ Jul 19 at 21:53
  • $\begingroup$ Universe's three dimensional isotropy is just unproven assumption made by Einstein to provide simplicity (in lack of exact knowledge of Universe's actual structure, especially beyond the "visible" part of it). If what I have read that the measurements of the cosmic microwave background indicate that the Universe has a flat geometry on large scales is true, then this clearly contradicts Enstein's assumption that Universe is isotropic. $\endgroup$
    – Alex
    Jul 19 at 23:56
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    $\begingroup$ @Alex What to you mean? The CMB measurements confirm the isotropy on the large scale. However, there are small variations in the CMB energy data, about 1 part in 100,000 (once you compensate for the anisotropies caused by our motion relative to the comoving frame of the CMB). The famous CMB image has been processed specifically to make those tiny deviations visible. $\endgroup$
    – PM 2Ring
    Jul 20 at 5:53
  • $\begingroup$ @Alex "the Universe has a flat geometry on large scales" means the 3D spatial geometry is Euclidian, as opposed to being spherical or hyperbolic. It is orthogonal to the question of whether the universe is isotropic. (Although I suspect you might have prolems in GR reconciling a strongly anisotropic distribution of matter with a homogeneous geometry, flat or otherwise. So the fact that the large-scale geometry appears to be homogeneously "flat" may require istrophy.) $\endgroup$ Jul 20 at 12:46
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An old conundrum was why do rotating galaxies and galaxy clusters not fly apart due to centrifugal (or -petal as you prefer) force, as the gravity due to their observable mass is too small to prevent this. The advent of dark matter (and energy) helped to explain this. If the universe is rotating, their gravitational force may prevent rotation adding to its expansion, especially since they seem to be evenly distributed throughout the universe.

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    $\begingroup$ This answer seems to be more speculation than mainstream physics. Why do you think galactic rotation has any bearing on cosmological rotation? $\endgroup$ Jul 15 at 16:47
  • $\begingroup$ @DeeGee May be with the assumption of rotating Universe and the centrifugal force caused by this rotation there will not be the need to introduce concepts of Dark Matter and Dark Energy? $\endgroup$
    – Alex
    Jul 15 at 18:44
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    $\begingroup$ @Alex I really hadn't thought this through. The gravitational attraction of dark matter might be enough to retain mass at the rotation centre but as it is evenly distributed, it would have little effect in preventing expansion further out where the angular velocity would be huge. $\endgroup$
    – DeeGee
    Jul 15 at 21:12
  • $\begingroup$ @DeeGee You are considering the existence of dark matter as a proven fact, while it is just a theoretical concept which has been introduced to explain gravitational lensing. Likewise the dark energy is just a theoretical concept introduced to explain red shift acceleration... $\endgroup$
    – Alex
    Jul 15 at 22:24
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    $\begingroup$ @Alex Dark matter is on much firmer ground than dark energy. We're pretty certain it exists, we just don't know what the hell it is. $\endgroup$
    – Ingolifs
    Jul 15 at 23:28
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Any and all movement is with respect to something else. If you were the only thing in the Universe, you would not know if you’re moving or not, because you would not have any reference point to define this movement from.

The same holds for the Universe itself. It is expanding, that we know by looking at galaxies and seeing that most of them have a redshift. But it would be wrong to think of the Universe as an inflating balloon, because there’s an outside to the balloon—now if there is an outside to the Universe, we don’t and we can’t know about it, so it’s in the domain of metaphysics, not physics or astronomy.

So, then, what would the Universe be moving or rotating relative to? The mere notion of Universe “rotation” has no meaning, because there is no “exterior” to compare it with. And no, we can’t say that it’s moving relative to itself, because then, there’s no movement (just like we couldn’t know the Earth is turning if there were no objects outside of it to define rotation).

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    $\begingroup$ Even without external reference, the rotation of the Earth can be detected, and measured, through the precession of gyroscopes or Foucault pendulums. $\endgroup$
    – notovny
    Jul 18 at 10:44
  • $\begingroup$ Because it rotates with respect to something else. It rotates with respect to the space around it. But there is nothing around the Universe. $\endgroup$ Jul 19 at 1:58
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    $\begingroup$ There are rotating solutions to the Einstein Field Equations, the first one was found by Kurt Gödel. So a universe could have global rotation without the need for something external that it's rotating relative to. However, the Gödel solution has closed timelike curves, which are pretty weird. ;) FWIW, Einstein was rather displeased to learn of the Gödel solution, mostly because of the CTCs. $\endgroup$
    – PM 2Ring
    Jul 20 at 5:42

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