On the Issue of the ζ series convergence and loop corrections in the generation of observable primordial non-Gaussianity in slow-roll inflation. II. The trispectrum

We calculate the trispectrum Tζ of the primordial curvature perturbation ζ, generated during a slow-roll inflationary epoch by considering a two-field quadratic model of inflation with canonical kinetic terms. We consider loop contributions as well as tree-level terms, and show that it is possible to attain very high, including observable, values for the level of non-Gaussianity τNL if Tζ is dominated by the one-loop contribution. Special attention is paid to the claim in J. Cosmol. Astropart. Phys. 02 (2009) 017 that, in the model studied in this paper and for the specific inflationary trajectory we choose, the quantum fluctuations of the fields overwhelm the classical evolution. We argue that such a claim actually does not apply to our model, although more research is needed in order to understand the role of quantum diffusion. We also consider the probability that an observer in an ensemble of realizations of the density field sees a non-Gaussian distribution. In that respect, we show that the probability associated to the chosen inflationary trajectory is non-negligible. Finally, the levels of non-Gaussianity fNL and τNL in the bispectrum Bζ and trispectrum Tζ of ζ, respectively, are also studied for the case in which ζ is not generated during inflation.