A rotating universe would produce anisotropies in the cosmic microwave background. WMAP data tightly constrains how much [if any] rotation may be present. After a little digging, I found the paper I had in mind:
http://arxiv.org/abs/0902.4575
Is the universe rotating?
Shi-Chun Su, M.-C. Chu
Models of a rotating universe have been studied widely since Godel {1}, who showed an example that is consistent with General Relativity (GR). By now, the possibility of a rotating universe has been discussed comprehensively in the framework of some types of Bianchi's models, such as Type V, VII and IX {2,3}, and different approaches have been proposed to constrain the rotation. Recent discoveries of some non-Gaussian properties of the Cosmic Microwave Background Anisotropies (CMBA) {nG1,nG2,nG3,nG4,nG5,nG6,nG7}, such as the suppression of the quadrupole and the alignment of some multipoles draw attention to some Bianchi models with rotation {bi1,bi2}. However, cosmological data, such as those of the CMBA, strongly prefer a homogeneous and isotropic model. Therefore, it is of interest to discuss the rotation of the universe as a perturbation of the Robertson-Walker metric, to constrain the rotating speed by cosmological data and to discuss whether it could be the origin of the non-Gaussian properties of the CMBA mentioned above. Here, we derive the general form of the metric (up to 2nd-order perturbations) which is compatible with the rotation perturbation in a flat Lambda-CDM universe. By comparing the 2nd-order Sachs-Wolfe effect {4,5,6,7,8} due to rotation with the CMBA data, we constrain the angular speed of the rotation to be less than $10^{-9}$ rad yr$^{-1}$ at the last scattering surface. This provides the first constraint on the shear-free rotation of a Lambda-CDM universe.