Full trispectrum in single field DBI inflation

Abstract

We compute the tree-level connected four-point function of the primordial curvature perturbation for a fairly general minimally coupled single field inflationary model, where the inflaton's Lagrangian is a general function of the scalar field and its first derivatives. This model includes K-inflation and DBI-inflation as particular cases. We show that, at the leading order in the slow-roll expansion and in the small sound speed limit, there are two important tree-level diagrams for the trispectrum. One is a diagram where a scalar mode is exchanged and the other is a diagram where the interaction occurs at a point, i.e. a contact interaction diagram. The scalar exchange contribution is comparable to the contact interaction contribution. For the DBI-inflation model, in the so-called equilateral configuration, the scalar exchange trispectrum is maximized when the angles between the four momentum vectors are equal and in this case the amplitude of the trispectrum from the scalar exchange is one order of magnitude higher than the contact interaction trispectrum.

Conformal invariance and the four point scalar correlator in slow-roll inflation

“…Two reviews which discuss non-Gaussianity from the CMB and from large scale structure are, [7], and [8] respectively. The scalar four point function in single field inflation has been discussed in [3,[9][10][11][12]. The general approach we adopt is along the lines of the seminal work of Maldacena [13].…”

Large nonlocal non-Gaussianity from a curvaton brane

“…For the trispectrum, as shown in [39,40], the correlation function includes a scalar propagation part and a contact interaction part. The detailed shape is complicated.…”

The trispectrum as a diagnostic of primordial orthogonal non-Gaussianities

“…The same reasoning shows that B of order one is technically natural as well. Note also that, as the effective field theory of inflation with operators involving only powers of δg 00 is computationally equivalent to k-inflation, it should not come as a surprise that the Lagrangian (2.6) can be identified with the one in [15,20] (see also [21]), with the correspondence, at leading order in 1/c 2 s :…”

“…(2.6) are of the same order as the one inπ 4 , they cancel in the quartic Hamiltonian at leading order in the small sound speed limit, leaving only the scalar exchange contributions T si and the contact-interaction trispectrum T c1 generated from the operator inπ 4 (see [24] for the first calculation of T c1 ). A detailed analysis of the shapes of the four constituent trispectra in (2.9) was performed in [15], to which we refer the reader for more details (see also [21]). Overall, they reached the conclusion that they all share very similar properties.…”