1.*
Department of Astrophysical Sciences, Princeton University,
Princeton, NJ 08544, USA
*

2.*
Astronomical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan
*

3.*
Department of Physics, Princeton University,
Princeton, NJ 08544, USA*

4.*
W. M. Keck Distinguished Visiting Professor,
School of Natural Sciences, Institute for Advanced Study,
Princeton, NJ 08540, USA
*

5.*
Max Planck Institut fur Astrophysik, Karl Schwarzschild Strasse 1,
D-85740 Garching bei Munchen, Germany*

6.*
European Southern Observatory, Karl Schwarzschild Strasse 2,
D-85740 Garching bei Munchen, Germany*

7.*
Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland
*

Abstract

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 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.

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Mail: ekomatsu@princeton.edu