Trispectrum estimator in equilateral type non-Gaussian models

We investigate an estimator to measure the primordial trispectrum in equilateral type non-Gaussian models such as k-inflation, single field DBI inflation and multi-field DBI inflation models from Cosmic Microwave Background (CMB) anisotropies. The shape of the trispectrum whose amplitude is not constrained by the bispectrum in the context of effective theory of inflation and k-inflation is known to admit a separable form of the estimator for CMB anisotropies. We show that this shape is $87 \%$ correlated with the full quantum trispectrum in single field DBI inflation, while it is $33 \%$ correlated with the one in multi-field DBI inflation when curvature perturbation is originated from purely entropic contribution. This suggests that $g_{\rm NL} ^{equil}$, the amplitude of this particular shape, provides a reasonable measure of the non-Gaussianity from the trispectrum in equilateral non-Gaussian models. We relate model parameters such as the sound speed, $c_s$ and the transfer coefficient from entropy perturbations to the curvature perturbation, $T_{\mathcal{R} S}$ with $g_{\rm NL} ^{equil}$, which enables us to constrain model parameters in these models once $g_{\rm NL}^{equil}$ is measured in WMAP and Planck.Comment: 19 pages, 4 figures. Accepted for publication in JCA

On the full quantum trispectrum in multi-field DBI inflation

We compute the leading order connected four-point function of the primordial curvature perturbation coming from the four-point function of the fields in multi-field DBI inflation models. We confirm that the consistency relations in the squeezed limit and in the counter-collinear limit hold as in single field models thanks to special properties of the DBI action. We also study the momentum dependence of the trispectra coming from the adiabatic, mixed and purely entropic contributions separately and we find that they have different momentum dependence. This means that if the amount of the transfer from the entropy perturbations to the curvature perturbation is significantly large, the trispectrum can distinguish multi-field DBI inflation models from single field DBI inflation models. A large amount of transfer $T_{\mathcal{RS}} \gg 1$ suppresses the tensor to scalar ratio $r \propto T_{\mathcal{RS}}^{-2}$ and the amplitude of the bispectrum $f_{NL}^{equi} \propto T_{\mathcal{RS}}^{-2}$ and so it can ease the severe observational constraints on the DBI inflation model based on string theory. On the other hand, it enhances the amplitude of the trispectrum $\tau_{NL}^{equi} \propto T_{\mathcal{RS}}^2 f_{NL}^{equi 2}$ for a given amplitude of the bispectrum.Comment: 22 pages, 10 figures, minor corrections, references are added, published version in PR

Primordial non-Gaussianity from the DBI Galileons

We study primordial fluctuations generated during inflation in a class of models motivated by the DBI Galileons, which are extensions of the DBI action that yield second order field equations. This class of models generalises the DBI Galileons in a similar way with K-inflation. We calculate the primordial non-Gaussianity from the bispectrum of the curvature perturbations at leading order in the slow-varying approximations. We show that the estimator for the equilateral-type non-Gaussianity, $f_{\rm NL} ^{equil}$, can be applied to measure the amplitude of the primordial bispectrum even in the presence of the Galileon-like term although it gives a slightly different momentum dependence from K-inflation models. For the DBI Galileons, we find $-0.32 /c_s^2 < f_{\rm NL} ^{equil} < -0.16/c_s^2$ and large primordial non-Gaussianities can be obtained when $c_s$ is much smaller than 1 as in the usual DBI inflation. In G-inflation models, where a de Sitter solution is obtained without any potentials, the non-linear parameter is given by $f_{\rm NL}^{equil} = 4.62 r^{-2/3}$ where $r$ is the tensor to scalar ratio, giving a stringent constraint on the model.Comment: 10 pages, 1 figure. Accepted for publication in PR