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We calculate the trispectrum T_\zeta of the primordial curvature perturbation\zeta, generated during a {\it slow-roll} inflationary epoch by considering atwo-field quadratic model of inflation with {\it canonical} kinetic terms. Weconsider loop contributions as well as tree level terms, and show that it ispossible to attain very high, {\it including observable}, values for the levelof non-gaussianity \tau_{NL} if T_\zeta is dominated by the one-loopcontribution. Special attention is paid to the claim in JCAP {\bf 0902}, 017(2009) [arXiv:0812.0807 [astro-ph]] that, in the model studied in this paperand for the specific inflationary trajectory we choose, the quantumfluctuations of the fields overwhelm the classical evolution. We argue thatsuch a claim actually does not apply to our model, although more research isneeded in order to understand the role of quantum diffusion. We also considerthe probability that an observer in an ensemble of realizations of the densityfield sees a non-gaussian distribution. In that respect, we show that theprobability associated to the chosen inflationary trajectory is non-negligible.Finally, the levels of non-gaussianity f_{NL} and \tau_{NL} in the bispectrumB_\zeta and trispectrum T_\zeta of \zeta, respectively, are also studied forthe case in which \zeta is not generated during inflation.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

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