Measurement of the Cosmic Microwave Background Bispectrum on theCOBEDMR Sky Maps

We measure the angular bispectrum of the cosmic microwave background (CMB)radiation anisotropy from the COBE Differential Microwave Radiometer (DMR)four-year sky maps. The angular bispectrum is the harmonic transform of thethree-point correlation function, analogous to the angular power spectrum, theharmonic transform of the two-point correlation function. First, we studystatistical properties of the bispectrum and the normalized bispectrum. We findthe latter more useful for statistical analysis; the distribution of thenormalized bispectrum is very much Gaussian, while the bare bispectrumdistribution is highly non-Gaussian. Then, we measure 466 modes of thenormalized bispectrum, all independent combinations of three-pointconfigurations up to a maximum multipole of 20, the mode corresponding to theDMR beam size. By measuring 10 times as many modes as the sum of previous work,we test Gaussianity of the DMR maps. We compare the data with the simulatedGaussian realizations, finding no significant detection of the normalizedbispectrum on the mode-by-mode basis. We also find that the previously reporteddetection of the normalized bispectrum is consistent with a statisticalfluctuation. By fitting a theoretical prediction to the data for the primaryCMB bispectrum, which is motivated by slow-roll inflation, we put a weakconstraint on a parameter characterizing non-linearity in inflation.Simultaneously fitting the foreground bispectra estimated from interstellardust and synchrotron template maps shows that neither dust nor synchrotronemissions significantly contribute to the bispectrum at high Galactic latitude.We conclude that the DMR map is consistent with Gaussianity.Comment: 26 pages, 8 figures. submitted to Astrophysical Journa