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 VIIₕ 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 σ/H₀<10^-9 and rotation ω/H₀<6×10^-8 for 0.1<~Ω₀<~1.