First‐Year Wilkinson Microwave Anisotropy Probe ( WMAP ) Observations: Tests of Gaussianity

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Abstract
We present limits to the amplitude of non-Gaussian primordial fluctuations in the WMAP 1 yr cosmic microwave background sky maps. A nonlinear coupling parameter, fNL, characterizes the amplitude of a quadratic term in the primordial potential. We use two statistics: one is a cubic statistic which measures phase correlations of temperature fluctuations after combining all configurations of the angular bispectrum. The other uses the Minkowski functionals to measure the morphology of the sky maps. Both methods find the WMAP data consistent with Gaussian primordial fluctuations and establish limits, -58 < fNL < 134, at 95% confidence. There is no significant frequency or scale dependence of fNL. The WMAP limit is 30 times better than COBE and validates that the power spectrum can fully characterize statistical properties of CMB anisotropy in the WMAP data to a high degree of accuracy. Our results also validate the use of a Gaussian theory for predicting the abundance of clusters in the local universe. We detect a point-source contribution to the bispectrum at 41 GHz, bsrc = (9.5 ± 4.4) × 10-5 μK3 sr2, which gives a power spectrum from point sources of csrc = (15 ± 6) × 10-3 μK2 sr in thermodynamic temperature units. This value agrees well with independent estimates of source number counts and the power spectrum at 41 GHz, indicating that bsrc directly measures residual source contributions.