Cosmic microwave background bispectrum and slow roll inflation

Abstract

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 ${\cal C}_{\ell_1 \ell_2 \ell_3}$ 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 $\ell_i$ 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 {\it 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-$\ell$'s considered for increasing multipole $\ell$ while the opposite applies for the standard ${\cal C}_{\ell}$'s.