An Almost Isotropic Cosmic Microwave Temperature Does Not Imply an Almost Isotropic Universe

In this Letter we will show that, contrary to what is widely believed, an almost isotropic cosmic microwave background (CMB) temperature does not imply that the universe is "close to a Friedmann-Lemaitre universe." There are two important manifestations of anisotropy in the geometry of the universe: (1) the anisotropy in the overall expansion, and (2) the intrinsic anisotropy of the gravitational field, described by the Weyl curvature tensor; the former usually receives more attention than the latter in the astrophysical literature. Here we consider a class of spatially homogeneous models for which the anisotropy of the CMB temperature is within the current observational limits but whose Weyl curvature is not negligible, i.e., these models are not close to isotropy even though the CMB temperature is almost isotropic.