The Limits on Cosmological Anisotropies and Inhomogeneities from COBE Data

Assuming that the cosmological principle holds, Maartens, Ellis and Stoeger (MES) recently constructed a detailed scheme linking anisotropies in the cosmic background radiation (CMB) with anisotropies and inhomogeneities in the large scale structure of the universe and showed how to place limits on those anisotropies and inhomogeneities simply by using CMB quadrupole and octupole limits. First we indicate and discuss the connection between the covariant multipole moments of the temperature anisotropy used in the MES scheme and the quadrupole and octupole results from COBE. Then we introduce those results into the MES limit equations to obtain definite quantitative limits on the complete set of cosmological measures of anisotropy and inhomogeneity. We find that all the anisotropy measures are less than 10−4 in the case of those not affected by the expansion rate H , and less than 10−6 Mpc−1 in the case of those which are. These results quantitatively demonstrate that the observable universe is indeed close to Friedmann-Lemâitre-RobertsonWalker (FLRW) on the largest scales, and can be adequately modelled by an almost-FLRW model – that is, the anisotropies and inhomogeneities characterizing the observable universe on the largest scales are not too large to be considered perturbations to FLRW.