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We show in this paper that it is possible to attain very high, {\it includingobservable}, values for the level of non-gaussianity f_{NL} associated with thebispectrum B_\zeta of the primordial curvature perturbation \zeta, in asubclass of small-field {\it slow-roll} models of inflation with canonicalkinetic terms. Such a result is obtained by taking care of loop correctionsboth in the spectrum P_\zeta and the bispectrum B_\zeta. Sizeable values forf_{NL} arise even if \zeta is generated during inflation. Five issues areconsidered when constraining the available parameter space: 1. we must ensurethat we are in a perturbative regime so that the \zeta series expansion, andits truncation, are valid. 2. we must apply the correct condition for the(possible) loop dominance in B_\zeta and/or P_\zeta. 3. we must satisfy thespectrum normalisation condition. 4. we must satisfy the spectral tiltconstraint. 5. we must have enough inflation to solve the horizon problem.

journal of cosmology and astroparticle physics

On the Issue of the \zeta Series Convergence and Loop Corrections in the  Generation of Observable Primordial Non-Gaussianity in Slow-Roll Inflation.  Part I: the Bispectrum