THE LIMITS ON COSMOLOGICAL ANISOTROPIES AND INHOMOGENEITIES FROM COBEDATA

Assuming that the cosmological principle holds, Maartens, Ellis, & Sto eger (MES) recently constructed a detailed scheme linking anisotropies in the cosmic background radiation (CMB) with anisotropies and inhomo geneities in the large-scale structure of the universe and showed how to place limits on those anisotropies and inhomogeneities simply by us ing CMB quadrupole and octupole limits. First, we indicate and discuss the connection between the covariant multiple moments of the temperat ure 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 o f 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 t he case of those which are. These results demonstrate quantitatively t hat the observable universe is indeed close to Friedmann-Lemaitre-Robe rtson-Walker (FLRW) on the largest scales and can be modeled adequatel y by an almost-FLRW model-that is, the anisotropies and inhomogeneitie s characterizing the observable universe on the largest scales are not too large to be considered perturbations to FLRW.