Measurement of the Cosmic Microwave Background Bispectrum on the Cobe Dmr Sky Maps

We measure the angular bispectrum of the cosmic microwave background (CMB) radiation anisotropy from the COBE Differential Microwave Radiometer (DMR) fouryear sky maps. The angular bispectrum is the harmonic transform of the three-point correlation function, analogous to the angular power spectrum, the harmonic transform of the two-point correlation function. First, we study statistical properties of the bispectrum and the normalized bispectrum. We find the latter more useful for statistical analysis; the distribution of the normalized bispectrum is very much Gaussian, while the bare bispectrum distribution is highly non-Gaussian. Then, we measure 466 modes of the normalized bispectrum, all independent combinations of three-point configurations up to a maximum multipole of 20, the mode corresponding to the DMR 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 simulated Gaussian realizations, finding no significant detection of the normalized bispectrum on the mode-by-mode basis. We also find that the previously reported detection of the normalized bispectrum is consistent with a statistical fluctuation. By fitting a theoretical prediction to the data for the primary CMB bispectrum, which is motivated by slow-roll inflation, we put a weak constraint on a parameter characterizing non-linearity in inflation. Simultaneously fitting the foreground bispectra estimated from interstellar dust and synchrotron template maps shows that neither dust nor synchrotron emissions significantly contribute to the bispectrum at high Galactic latitude. We conclude that the DMR map is consistent with Gaussianity. Subject headings: cosmology: observations – cosmic microwave background – early universe Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA Astronomical Institute, Tôhoku University, Aoba, Sendai 980-8578, Japan Department of Physics, Princeton University, Princeton, NJ 08544, USA W. M. Keck Distinguished Visiting Professor, School of Natural Sciences, Institute for Advanced Study, NJ 08540, USA Max Planck Institut für Astrophysik, Karl Schwarzschild Strasse 1, D-85740 Garching bei München, Germany European Southern Observatory, Karl Schwarzschild Strasse 2, D-85740 Garching bei München, Germany Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland