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Solar-system measurements put a model-independent upper limit on the rate of rotation of the universe of about 10^-8 rad/yr: Clemence, C.M. (1957). 'Astronomical Time', Rev. Mod. Phys. Vol. 29, p. 2
Measurements of correlations in the CMB can also be used to impose an upper limit, but this is model-dependent. Two papers on this are:
-Barrow, J. D., Juszkiewicz, R., & Sonoda, D. H., "Universal rotation: how large
can it be?," 1985 -- http://adsabs.harvard.edu/full/1985MNRAS.213..917B
-Su and Chu, "Is the universe rotating?," 2009, http://arxiv.org/abs/0902.4575
Barrow's limit comes out to be 10^-15 rad/yr (assuming a flat universe, which we now know to be the case), whereas Su and Chu's is 10^-9 rad/yr. So 24 years later, the upper limit appears to have been relaxed by a factor of a million. Is this (a) because Barrow messed up, or (b) because it's model-dependent, and Barrow makes different assumptions than Su?
Measurements of correlations in the CMB can also be used to impose an upper limit, but this is model-dependent. Two papers on this are:
-Barrow, J. D., Juszkiewicz, R., & Sonoda, D. H., "Universal rotation: how large
can it be?," 1985 -- http://adsabs.harvard.edu/full/1985MNRAS.213..917B
-Su and Chu, "Is the universe rotating?," 2009, http://arxiv.org/abs/0902.4575
Barrow's limit comes out to be 10^-15 rad/yr (assuming a flat universe, which we now know to be the case), whereas Su and Chu's is 10^-9 rad/yr. So 24 years later, the upper limit appears to have been relaxed by a factor of a million. Is this (a) because Barrow messed up, or (b) because it's model-dependent, and Barrow makes different assumptions than Su?