Cosmic microwave background bispectrum and slow roll inflation

Recent tentative findings of non-Gaussian structure in the COBE-DMR dataset have triggered renewed attention to candidate models from which such intrinsic signature could arise. In the framework of slow roll inflation with built-in non linearities in the inflaton field evolution we present expressions for both the cosmic microwave background (CMB) skewness and the full angular bispectrum C`1`2`3 in terms of the slow roll parameters. We use an estimator for the angular bispectrum recently proposed in the literature and calculate its variance for an arbitrary `i multipole combination. We stress that a real detection of non-Gaussianity in the CMB would imply that an important component of the anisotropies arises from processes other than primordial quantum fluctuations. We further investigate the behavior of the signal-to-(theoretical) noise ratio and demonstrate for generic inflationary models that it decreases in the limited range of small-`’s considered for increasing multipole ` while the opposite applies for the standard C`’s.