Hunting for primordial non-Gaussianity in the cosmic microwave background

Since the first limit on the (local) primordial non-Gaussianity parameter, f(NL), was obtained from the Cosmic Background Explorer (COBE) data in 2002, observations of the cosmic microwave background (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 data of the Wilkinson Microwave Anisotropy Probe (WMAP) is f(NL) = 32 +/- 21, and the Planck satellite is expected to reduce the uncertainty by a factor of 4 in a few years from now. If f(NL) >> 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 f(NL) similar to 30, then it would be able to test a broad class of multi-field models using the 4-point function (trispectrum) test of tau(NL) >= (6f(NL)/5)(2). In this paper, 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.