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Suppose in the milliseconds after the big bang the cosmic egg had aquired some large angular momentum. As it expanded, keeping the momentum constant (not external forces) the rate of rotation would have slowed down, but it would never reach zero.

What implications would that have to measurments to distant supernova and CMB radiation? Do we have any experimental data that definitely rules out such as scenario? And to what confidence level?

Edit A Recent Article suggests that the universe might indeed be spinning as a whole. Anyone care to poke holes at it?

Edit 2 Even more Recent Article places limits on possible rotation.

Edit 3 Apparently Gödel pondered the same question ( https://www.space.com/rotating-universe-would-permit-time-travel)

John Alexiou
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    I'm interested to see the answers. However, my first thought is "rotating relative to what?" I'm not so sure it's meaningful to talk about the entire universe rotating. – Tim Goodman Nov 18 '10 at 07:46
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    What about Gödel's solution, Tim? It's true that one of the motivations for Einstein to construct GR was the Machian principle, but it turns out that GR allows geometries that violate the principle. – Raskolnikov Nov 18 '10 at 07:51
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    @Raskolnikov: Good point with the Gödel metric – Tim Goodman Nov 18 '10 at 10:04
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    @Tim: While linear motion is relative, it is not true about angular motion. – Piotr Migdal Nov 18 '10 at 10:13
  • @Tim: there is certainly no problem with that. The reason these solutions don't pop up often is that for localized systems one usually requires asymptotic flatness (or dS or AdS) while for the universe as a whole one often requires homogeneity. The assumptions can surely be dropped but I am not sure anything reasonable can then be said about the solutions (they might not be easy to find anyway). – Marek Nov 18 '10 at 10:38
  • @Piotr: Can you elaborate on what you mean by "angular motion is not relative"? I guess I would have said the Earth is rotating relative to the distant stars, but not relative to me as I sit on its surface. Are you referring to the fact that the rotating frame is not inertial? Or is your point related to rotating metrics in GR such as Raskolnikov mentioned? Or something else? – Tim Goodman Nov 18 '10 at 17:15
  • Godel's solution requires a fixed (constant) rotation I think. What about if there is a distribution of angular momentum, like a galaxy. – John Alexiou Nov 19 '10 at 05:33
  • The Gödel metric does not describe an expanding universe, so I think it doesn't really answer the question, which implies expansion. http://en.wikipedia.org/wiki/G%C3%B6del_metric#Cosmological_Interpretation – Sklivvz Nov 21 '10 at 13:16
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    The discovery.com article links to the actual paper: http://arxiv.org/abs/1104.2815 If this is right, then I guess it would be the first possible hint of a nonzero rate of rotation for the universe. He doesn't attempt to state his results in terms of an angular velocity. I doubt that this type of anisotropy is consistent with inflation...? –  Jul 26 '11 at 01:10
  • Edit#2 with link to article stating the odds of rotation are 1:121000 – John Alexiou Sep 22 '16 at 02:43
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    @TimGoodman Even more realistically, the Kerr solution describes a rotating universe which is even empty. – AGML Sep 22 '16 at 05:06
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    I would upvote this question, but I don't think it would do it any justice to disrupt the 42 score – lurscher Feb 20 '18 at 21:02
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    In 1984 I brought the question to John Archibald Wheeler. My proposal was that a global rotation of the Universe could explain the asymmetry of messon decay, and the prevalence of matter of anti-matter which resulted in the material Universe. – Steven Thomas Hatton Feb 20 '18 at 21:10
  • Every other particles or system can rotate and is inside something else. There’s a good chance the universe does too. Or at least no reason to assume it doesn’t. – Bill Alsept Feb 20 '18 at 21:17
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    @TimGoodman --It's a little "late in the day", but, re your question (in these comments) "fixed relative to what?", an answer (basically, "fixed relative to expanding space") is provided in the 2019 paper at https://arxiv.org/pdf/1910.10819.pdf . – Edouard Jan 03 '21 at 20:51
  • I've got to add the fact that the cosmological model in which the aforementioned answer to Tim's question is described differs a little from Godel's (as it's based on Einstein-Cartan theory rather than GR), although, since it appears to be set within Kerr-Newman black holes (which contain the closed timelike curves whose traversal would require a lot of time and energy), I'd guess it has a lot of similarities to it. – Edouard Jan 03 '21 at 21:10
  • A more recent result, based on an analysis of some 200 spiral galaxies which found one direction of rotation to be preferred to another by a factor of 2%, was released in mid-2020, and is sketched at https://www.newscientist.com/article/2244998-the-entire-universe-may-once-have-been-spinning-all-over-the-place/ . – Edouard Mar 26 '21 at 20:20
  • At en.wikipedia.org/wiki/Axis_of_evil_(cosmology) , the "Axis of Evil" implications interpreting any preferred direction of motion as a psychological "idea of reference" might as well be interpreted as a denial of the obvious fact that ANY preferred direction of motion may occur within a LOCAL universe, in a multiverse (divided into causally-separated regions by the event horizons of the black holes within which LUs may develop) that's favored by the "Black Hole Genesis" models developed by Smolin, Poplawski, etc. They seem to be missing the possibility of a categorical division. – Edouard – Edouard Mar 26 '21 at 21:02

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If you believe wholeheartedly in Mach's principle, then there is no way to test empirically for rotation of the universe as a whole, since there is nothing else for it to be rotating relative to. However, general relativity is not very Machian, and it offers a variety of ways in which an observer inside a sealed laboratory can detect whether the lab is rotating. For example, she can observe the motion of a gyroscope, or measure whether the Sagnac effect is zero. There are alternative theories of gravity, such as Brans-Dicke gravity, that are more Machian than GR,[Brans 1961] and in these theories there is probably no meaningful sense in which the universe could rotate. However, solar-system tests[Bertotti 2003] rule out any significant deviations from GR of the type predicted by Brans-Dicke gravity, so that it appears that the universe really is as non-Machian as GR says it is.

It is therefore possible according to general relativity to have cosmologies in which the universe is rotating. Historically, one of the earliest cosmological solutions to the Einstein field equations to be discovered was the Gödel metric, which rotates and has closed timelike curves. If we lived in a rotating universe such Gödel's example, the rate of rotation would have to be expressed in terms of angular velocity, not angular momentum. Angular velocity is what is measured by a gyroscope or the Sagnac effect, and GR doesn't even have a definition of angular momentum that applies to cosmological spacetimes.

A rotating universe does not have to have a center of rotation, and it can be homogeneous. In other words, we could determine a direction in the sky and say that the universe was rotating counterclockwise at a certain rate about the line connecting us to that point on the celestial sphere. However, aliens living somewhere else in the universe could do the same thing. Their line would be parallel to ours, but there would be no way to tell whether one such line was the real center of rotation.

To find out whether the universe is rotating, in principle the most straightforward test is to watch the motion of a gyroscope relative to the distant galaxies. If it rotates at an angular velocity -ω relative to them, then the universe is rotating at angular velocity ω. In practice, we do not have mechanical gyroscopes with small enough random and systematic errors to put a very low limit on ω. However, we can use the entire solar system as a kind of gyroscope. Solar-system observations put a model-independent upper limit of 10^-7 radians/year on the rotation,[Clemence 1957] which is an order of magnitude too lax to rule out the Gödel metric.

A rotating universe must have a certain axis of rotation, so it must have a particular type of anisotropy that picks out a certain preferred direction. We can therefore look at the cosmic microwave background and see whether its anisotropy contains a preferred axis.[Collins 1973] Such observations impose a limit that is tighter than provided by solar-system measurements (perhaps 10^-9 rad/yr[Su 2009] or 10^-15 rad/yr[Barrow 1985]), but such limits are model-dependent.

Because all of the present observation are consistent with zero rotational velocity, it is not possible to attribute any prominent cosmological role to rotation. Centrifugal forces cannot contribute significantly to cosmological expansion, or to the way your head feels when you're hung over.

Brans and Dicke, "Mach's principle and a relativistic theory of gravitation," Phys. Rev. 124 (1961) 925, http://loyno.edu/~brans/ST-history/

Bertotti, Iess, and Tortora, "A test of general relativity using radio links with the Cassini spacecraft," Nature 425 (2003) 374

Clemence, "Astronomical time," Rev. Mod. Phys. Vol. 29 (1957) 2

Collins and Hawking, "The rotation and distortion of the universe," Mon. Not. R. Astr. Soc. 162 (1973) 307

Hawking, "On the rotation of the universe," Mon. Not. R. Astr. Soc. 142 (1969) 529

Barrow, Juszkiewicz, and Sonoda, "Universal rotation: how large can it be?," Mon. Not. R. Astr. Soc. 213 (1985) 917, http://adsabs.harvard.edu/full/1985MNRAS.213..917B

Su and Chu, "Is the universe rotating?," 2009, http://arxiv.org/abs/0902.4575

[This is a physicsforums FAQ entry that I wrote with input from users George Jones, jim mcnamara, marcus, PAllen, tiny-tim, and vela.]

  • Hi Ben. "Their line would be parallel to ours, but there would be no way to tell whether one such line was the real center of rotation." interesting, so a given object between the line joining both 'axes' (ours and those of the aliens) how would it displace due to universal rotation? How does this global rotation manifests in close objects? I understand that cosmological expansion manifests as galaxies increasing their distance locally, but i'm not clear what local consequences does this rotation have – lurscher Jun 07 '13 at 21:41
  • @lurscher: Every inertial observer would see himself as being at rest and the universe as rotating about an axes through him. I had observers A and B. If you add a third object C, it's still the same story. Each of the three says the other two rotate about the axis passing through him. "Locally..." I guess it depends on how local you mean by local. Expansion isn't locally detectable either, unless you have a very charitable definition of local. –  Jun 08 '13 at 01:09
  • Ben, i can in principle make a very long material thread, send it to another galaxy, and i should be able to extract work from the cosmological expansion.

    In a similar way, if a region has constant non-zero positive curvature, i should be able to create (again, in principle) a really big triangle with the same thread, but the inner angles of the triangle would sum above $\pi/2$

     – lurscher Jun 08 '13 at 01:33
  • I was hoping that the rotation would in principle mean that one of those threads, if put far way, would wind around another thread in a given direction, but it seems is not as simple as that – lurscher Jun 08 '13 at 01:34
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    "A rotating universe must have a certain axis of rotation" - Actually, rotation is defined mathematically in a plane, but not "around an axis". For example, if spatially the universe is a 3-sphere (the hypersurface of a 4D ball), then it could rotate in two orthogonal planes simultaneously while no axis of either rotation can be defined (and even with just one rotation the axis is outside the physical manifold). An easier example to visualize is a rotation in a 2D plane where no axis exists. An axis can be defined only in special cases and does not necessarily have to exist for the universe. – safesphere Nov 16 '19 at 17:33
  • @safesphere As I can draw, I see what you're saying (in spite of my limited mathematical knowledge), but, especially because the curvature of spatial rotations might be infinitesimally small (and, consequently, inherently unobservable) in a spatially infinite universe or multiverse, do you feel that your conclusions imply that Nikodem J. Poplawski's claim that his theory of cosmological genesis within black holes is scientific (i.e., that it can be falsified) is dependent upon such temporal rotation as might be evidenced by recurrent or simultaneous events within a single gravitational field? – Edouard Apr 26 '20 at 18:11
  • (Poplawski has felt that an absence of evidence of universal rotation would falsify his theory, and, as black holes are local, the universes concerned--including our own--would each be local.) – Edouard Apr 26 '20 at 18:20
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    @Edouard Your question sounds like a good one to post as a separate question to get the expert insight of those more familiar with the torsion gravity. You'd also have more room there to explain more clearly what your question is. My comment above simply states that not every rotation has an axis. However, the absence of an axis doesn't make rotation undetectable. On $S^2$, you can be static at the North Pole observing the globe rotating or you can be at the equator rotating with the globe. On $S^3$, you can be at the North Pole of one rotation and on the equator of another at the same time. – safesphere Apr 27 '20 at 19:00
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I think in that case the universe will be homogeneous but not isotropic. Such geometries were classified by Bianchi, and they have parameters that are constrained be experiment (not my area of expertise, so I am not sure to what degree). As far as I know, there is no indication that angular momentum is needed to explain any cosmological observation.

Incidentally, I don't think general relativity (or any other current theory) obeys Mach's principal, as usually phrased it requires highly non-local effects. Frame dragging may be in the spirit of Mach's principle, but it follows from perfectly local interactions as encoded in GR.

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I am not sure about the Lense-Thirring effect in this case, but it is definitely true that a global rotation would be described by one of the Bianchi homogeneous but anisotropic (not isotropic) models as mentioned by Moshe. For beautiful pictures as to how the Cosmic Microwave Background anisotropy sky would look in those models, see the paper by Andrew Pontzen for example (Pontzen 2009).

Using the current CMB data, especially from the WMAP experiment, one can impose upper bounds on (and perhaps some day, detections of) those Bianchi models. This work goes at least as far back as Ted Bunn and collaborators' paper (Bunn, Fereira & Silk 1996)

Dragan Huterer
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    Thanks for mentioning my old paper! There are, not surprisingly, a bunch of better limits since our time. The constraints on the rotation of the Universe are very strict. – Ted Bunn Jan 15 '11 at 18:41
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Mach's principle says that inertia arises from the mass of everything else in the universe, and so if the universe were rotating, it would be dragging us around in a circle with it, and because of that we wouldn't notice it. This frame-dragging actually happens, and is called the Lense-Thirring effect. If you were inside a massive rotating sphere, your frame of reference would be rotating with respect the rest of the universe outside the massive rotating sphere. However, I'm not sure whether the Lense-Thirring effect actually implies Mach's principle. Maybe somebody who knows more could help.

Peter Shor
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  • Actually the sphere example is not a very good representation of space because of the vast distance. In a casual sphere you can say that the outer shell simply has more linear velocity than the inner shells, but when universe is in question, after a point you'd need velocities faster than light just to keep up with the angular speed w.r.t to the rotation axis. – Cem Nov 18 '10 at 15:26
  • It's not clear this kind of argument works with general relativity. If you look at Kerr black holes, some of the space inside of a rotating black hole is rotating so fast because of frame dragging that an object cannot stand still with respect to the space outside the black hole. – Peter Shor Nov 18 '10 at 19:12
  • The classic paper on the kind of thing you're talking about is C. Brans and R. H. Dicke, Physical Review 124 (1961) 925, http://loyno.edu/~brans/ST-history/ It's very readable. –  Jul 26 '11 at 00:57
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If you say that universe is rotating "as a whole" you'd have to define a rotation axis. A rotation axis would cause some problems, like violating a homogeneous and isotropic universe, as proposed by cosmic inflation model.

By the way, you can not say that the universe is rotating at the same angular speed everywhere with respect to the rotation axis. This would cause faster than light linear velocities, although I simply used classical mechanics to calculate, maybe a relativistic model is possible.

The existence of such an angular momentum might have some implications though. For example, one could say, if the theory "Big Bounce"(http://en.wikipedia.org/wiki/Big_bounce) is correct, one could say the origin of the entire universe is a black hole with an angular momentum, that is, a rotating black hole with possibly no electrical charge.

Cem
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  • Yes a rotation axis, and this non-homogenous universe would be the implication (albeit, just slightly), but what evidence we would see to support or to shoot down this? It violates the inflation theory is not sufficient, because inflation is just a construct to explain the flatness of the universe, without much of a physical mechanism behind it (I may be wrong here). – John Alexiou Nov 19 '10 at 05:26
  • If the universe is rotating, in a classical sense, without a rotation axis, and it is somehow possible, via relativity, to be rotating with the same angular velocity everywhere, my answer would be: It does not matter. Because then, It would be stationary for every single observer in this universe. Then we can ask the question "Rotating with respect to who?" which would be a pretty damn speculative question in my opinion. However back to your initial question: If the rotation is in the classical sense, there is no way to understand from inside the universe. – Cem Nov 19 '10 at 11:10
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    You're reasoning based on your Newtonian intuition about rotation, and it's leading you to say things that aren't true in GR. You can have rotation with homogeneity. See, e.g., Barrow, J. D., Juszkiewicz, R., & Sonoda, D. H., "Universal rotation: how large can it be?," 1985 -- http://adsabs.harvard.edu/full/1985MNRAS.213..917B No, such a model does not lead to faster-than-c velocities. Worrying about >c velocities in this context doesn't make sense, because GR doesn't have a uniquely well-defined notion of the relative velocity of distant objects. –  Jul 26 '11 at 00:54
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Hoyle and Narlikar have also shown that rotation in fact decays for an expanding universe - which could potentially explain why if rotation exists, it appears to be very very slow (see Hawking's own remarks on this). It also explains why there would be no discernible axis of rotation. Dark flow could be a residual primordial spin to the universe (something I speculated a while back). Rotation also requires energy - there could have been a bulk-to-rotation exchange of energy which may explain the vacuum energy problem (bit of a reach but I found it hard not to mention it). Obviously a rotating universe early on would play a significant role in the expansion of a universe due to an internal centrifugal force. The universe appears to have got large enough not to be hindered by the gravitational binding forces inside of it. The following link https://gyroverse.quora.com/ is my own work, but gives a reasonable jist for an expanding universe.

Gareth Meredith
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    Rotation may require energy, but so does inflation. Yet one is dismissed and the other at least considered. – John Alexiou Feb 12 '18 at 13:11
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    @ja72 Hawking discusses vorticity http://adsabs.harvard.edu/full/1969MNRAS.142..129H ( for vorticity see https://en.wikipedia.org/wiki/Vorticity). It is how "rotation" appears in the four dimensions, and gives very low limit values for it from CMB observations, back in 1969. – anna v Feb 12 '18 at 14:15
  • Inflation will be replaced by something better, maybe even by an early rotary property. Inflation is being attacked right now, even by some of its founders stating that it naturally leads to a multiverse and its been argued this is not a scientific theory. So we need to start thinking about new alternatives. – Gareth Meredith Feb 13 '18 at 09:49
  • Hawking has made statements on whether the universe actually spins, stating clearly that if it does, it is remarkably slow. I'd like to find the relevant data for dark flow to test how slow that rotation truly needs to be without leaving a CMB print. I'll try and find his relevant statement. – Gareth Meredith Feb 13 '18 at 09:51
  • here we go: direct qoute Hawking :

    ''These models could well be a reasonable description of the universe we observe, however observational data are compatible only with a slow rotation.''

     – Gareth Meredith Feb 13 '18 at 09:59
  • Ja72, I'd be careful saying a spinning universe has been dismissed. The evidence I have seen suggests otherwise. – Gareth Meredith Feb 13 '18 at 10:04
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    Dear Gareth Meredith: For your information, Physics.SE has a policy that it is OK to cite oneself, but it should be stated clearly and explicitly in the answer itself, not in attached links. – Qmechanic Feb 16 '18 at 15:20
  • I beg your pardon, but I have been clear. All I did was link you to the math. But I have been very clear otherwise. – Gareth Meredith Feb 17 '18 at 15:10
  • Your answer does not say that the link is to your own work. It needs to say that the link is to your own work "clearly and explicitly in the answer itself, not in attached links". – dmckee --- ex-moderator kitten Feb 17 '18 at 16:57
  • I've deleted this post until you get around to address the disclosure issue. – dmckee --- ex-moderator kitten Feb 17 '18 at 19:34
  • By "disclosure issue" we mean: it should be unambiguous from the text of your answer whether the link you give is to work that you created. – rob Feb 19 '18 at 17:21
  • Stop flagging this post for undeletion. It has been explained to you multiple times that it must be clearly stated in the answer itself that you are the author of the resource you link. Comply with this or live with your post staying deleted. – ACuriousMind Feb 20 '18 at 20:20