I know that having a net angular momentum will contradict isotropy of the universe by preferring a specific direction. But is there any experimental data on the total angular momentum of the universe and how much it deviates from zero (perhaps according to the CM frame)?
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2possible duplicate of What if the universe is rotating as a whole? – Aug 04 '13 at 19:42
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I don't know the answer to this question, but I do know that the total angular momentum of a system could depend on your choice of reference frame and point of origin. (Although, I suppose it could be zero in every choice of coordinates too.)
Lets assume a classical universe containing a spinless particle. Pick a reference frame where the particle is moving with velocity $\vec{v}$. Rotate the coordinate system so that $v$ points parallel to the particle's position vector $\vec{r}$. Then the total angular momentum is zero. However, if you shift the origin so that $\vec{r}$ and $\vec{v}$ are no longer parallel, now you have a nonzero angular momentum.
However, there's an obvious choice of the origin: Earth, since we live on it. I'm not aware of any experiments that can measure the total angular momentum of the universe, and any such measurement will definitely have large error bars.
TheHamBox
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1As discussed in the answers to the question that this question duplicates, research on this question deals with angular velocity, not angular momentum. It doesn't make sense to ask the question in terms of angular momentum, because the structure of GR doesn't allow us to add up a tensor such as angular momentum over a cosmological spacetime. This kind of thing is discussed in Misner, Thorne, and Wheeler, p. 457. – Aug 04 '13 at 23:58
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