Anisotropy and inhomogeneity of the universe from ΔT/T

A recent paper (Martinez-Gonzalez & Sanz 1995) showed that if the universe is homogeneous but anisotropic, then the small quadrupole anisotropy in the cosmic microwave background radiation (CBR) implies that the spacetime anisotropy is very small. We point out that more general results may be established, assuming the weaker condition that all fundamental observers measure the CBR to be almost isotropic, instead of assuming that the universe is exactly homogeneous. Assuming this weak Copernican principle (which is partially testable), we have proved that if small anisotropies are observed in the CBR, then the observable universe is almost Friedmann-Robertson-Walker. Furthermore, the quadrupole and octopole place direct and explicit limits on the degree of anisotropy and inhomogeneity, as measured by the shear, vorticity, Weyl tensor and density gradients. (We follow the standard assumption that the CBR dipole is purely Doppler and may be removed by a velocity boost.) In the presence of inhomogeneity, it is only possible to set a much weaker limit on the shear than that given by Martinez-Gonzalez & Sanz.