Limits to global rotation and shear from the COBE DMR four-year sky maps

Small departures from a homogeneous isotropic spacetime create observable features in the large-scale anisotropy of the cosmic microwave background. We cross correlate the maps of the cosmic microwave background anisotropy from the Cosmic Background Explorer Differential Microwave Radiometers four-year data set with template maps from Bianchi type VII${}_h$ cosmological models to limit global rotation or shear in the early universe. On the largest scales, spacetime is well described by the Friedmann-Robertson-Walker metric, with departures from isotropy about each spatial point limited to shear $\sigma {/H}_0<{10}^{-9}$ and rotation $\omega {/H}_0<6\mathrm{}\times {10}^{-8}$ for $0.1<~{\Omega }_0<~1$.