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

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

2008-11-25

arxiv.org/abs/0811.4092v3

Phys.Rev.D81:023531,2010

Astronomy and Astrophysics

Astrophysics

LaTex File, 27 pages, 8 figures. v2: Previous Section 2 has been removed. Two new sections (3 and 4) discussing the classicali

Scientific paper

10.1103/PhysRevD.81.023531

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.

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