Is the universe rotating?
Abstract
Models of a rotating universe have been studied widely since G\"odel 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 -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 universe.