Cosmic Microwave Background Bispectrum and Slow Roll Inflation

Abstract

Recent tentative findings of non-Gaussian structure in the COBE-DMR data set have triggered renewed attention on 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 Cℓ1ℓ2ℓ3 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 ℓi 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 behaviour of the signal-to-(theoretical) noise ratio and demonstrate for generic inflationary models that it decreases in the limited range of small ℓs considered for increasing multipole ℓ, while the opposite applies for the standard Cℓs.