Hunting for Primordial Non-Gaussianity in the Cosmic Microwave Background

Since the first limit on the (local) primordial non-Gaussianity parameter, fNL, was obtained from COBE data in 2002, observations of the CMB have been playing a central role in constraining the amplitudes of various forms of non-Gaussianity in primordial fluctuations. The current 68% limit from the 7-year WMAP data is fNL=32+/-21, and the Planck satellite is expected to reduce the uncertainty by a factor of four in a few years from now. If fNL>>1 is found by Planck with high statistical significance, all single-field models of inflation would be ruled out. Moreover, if the Planck satellite finds fNL=30, then it would be able to test a broad class of multi-field models using the four-point function (trispectrum) test of tauNL>=(6fNL/5)^2. In this article, we review the methods (optimal estimator), results (WMAP 7-year), and challenges (secondary anisotropy, second-order effect, and foreground) of measuring primordial non-Gaussianity from the CMB data, present a science case for the trispectrum, and conclude with future prospects.Comment: 33 pages, 4 figures. Invited review, accepted for publication in the CQG special issue on nonlinear cosmological perturbations. (v2) References added. More clarifications are added to the second-order effect and the multi-field consistency relation, tauNL>=(6fNL/5)^2