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 ${\mathcal{C}}_{{\ell }_1{\ell }_2{\ell }_3}$ 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 ${\mathcal{C}}_{\ell }$'s.

15 pages, 3 figures, minor corrections Ref: MNRAS 313, 323 (2000)

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