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

TL;DR

This paper calculates the primordial trispectrum in a two-field slow-roll inflation model, exploring loop contributions, quantum fluctuation effects, and the probability of observable non-Gaussianity levels.

Contribution

It provides a detailed analysis of the trispectrum including loop effects and challenges previous claims about quantum fluctuations dominating classical evolution.

Findings

High non-Gaussianity levels achievable with one-loop dominance.

Quantum fluctuations do not necessarily overwhelm classical evolution in this model.

The probability of observing significant non-Gaussianity is non-negligible.

Abstract

We calculate the trispectrum T_\zeta of the primordial curvature perturbation \zeta, generated during a {\it slow-roll} inflationary epoch by considering a two-field quadratic model of inflation with {\it canonical} kinetic terms. We consider loop contributions as well as tree level terms, and show that it is possible to attain very high, {\it including observable}, values for the level of non-gaussianity \tau_{NL} if T_\zeta is dominated by the one-loop contribution. 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 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 f_{NL} and \tau_{NL} in the bispectrum B_\zeta and trispectrum T_\zeta of \zeta, respectively, are also studied for the case in which \zeta is not generated during inflation.