important feature of the simplest inflation models is that the primordial density fluctuation field has a Gaussian random phase distribution (Guth & Pi 1982; Hawking 1982; Starobinsky 1982; Bardeen, Steinhardt & Turner 1983; see Riotto 2002 for a review). Therefore, an observational test of the Gaussianity of the initial density fluctuation field will provide an important constraint on inflation models. Fortunately, the CMB temperature anisotropy, which reflects the density fluctuation on the last scattering surface, is expected to be the best probe of the primordial Gaussianity.

There have been many tests for the Gaussianity of the CMB anisotropy at large ($\sim 10\degr$; Kogut et al. 1996; Colley, Gott, & Park 1996; Ferreira, Magueijo, & Górski 1998; Heavens 1998; Pando, Valls-Gabaud, & Fang 1998; Novikov, Feldman, & Shandarin 1999; Bromley & Tegmark 1999; Magueijo 2000; Banday, Zaroubi, & Górski 2000; Mukherjee, Hobson, & Lasenby 2000; Barreiro et al. 2000; Aghanim, Forni, & Bouchet 2001; Phillips & Kogut 2001; Komatsu et al. 2002), intermediate ($\sim 1\degr$; Park et al. 2001; Shandarin et al. 2002), and small angular scales ($\sim 10\arcmin$; Wu et al. 2001; Santos et al. 2002, 2003; Polenta et al. 2002; De Troia et al. 2003). Most of the results 