Universal rotation: how large can it be?

We present a detailed analysis of the expected temperature distribution of the cosmic microwave background radiation in flat, open and closed universes possessing small anisotropics. We predict the most general temperature patterns on the sky and their associated angular correlation functions. We use these results to evaluate the largest level of cosmic vorticity compatible with existing observations of the dipole and quadrupole fluctuations in the microwave background. This analysis extends previous work by employing the quadrupole observations and calculating all observable quantities. It is found that the asymmetries in radio-source orientations measured by Birch cannot be due to universal rotation. Detailed limits on the allowed cosmic vorticity and large-scale velocity field are given for all possible homogeneous cosmological models close to isotropy. We also study in detail the geodesic spiralling effect predicted to occur in the most general flat and open homogeneous anisotropic universes. The nature of this feature is independent of the total density in these universes and offers a new means of determining by direct observation whether or not the Universe is closed no matter how close the density is to the critical density.