On the Issue of the ζ Series Convergence and Loop Corrections in the Generation of Observable Primordial Non-Gaussianity in Slow-Roll Inflation. Part I: the Bispectrum
Abstract
We show in this paper that it is possible to attain very high, including observable, values for the level of non-gaussianity fNL associated with the bispectrum Bζ of the primordial curvature perturbation ζ, in a subclass of small-field slow-roll models of inflation with canonical kinetic terms. Such a result is obtained by taking care of loop corrections both in the spectrum Pζ and the bispectrum Bζ. Sizeable values for fNL arise even if ζ is generated during inflation. Five issues are considered when constraining the available parameter space: 1. we must ensure that we are in a perturbative regime so that the ζ series expansion, and its truncation, are valid. 2. we must apply the correct condition for the (possible) loop dominance in Bζ and/or Pζ. 3. we must satisfy the spectrum normalisation condition. 4. we must satisfy the spectral tilt constraint. 5. we must have enough inflation to solve the horizon problem.