Primordial Trispectrum from Entropy Perturbations in Multifield DBI Model

TL;DR

This work analyzes the primordial trispectrum in a general multifield DBI inflation framework, where entropy perturbations can source curvature on superhorizon scales. It derives the four-point functions arising from scalar-exchanging interactions mediated by an adiabatic mode, focusing on the large transfer limit $T_{RS}\gg1$ and employing in-in techniques. The authors obtain analytic expressions for the relevant trispectrum components and study their momentum-space shapes in equilateral and specialized planar configurations, finding distinct features such as a $p_{13}\to0$ divergence in the equilateral case and a squeezed-limit peak in the planar case. These results provide templates for entropy-generated non-Gaussianities and potential observational discriminants between multifield and single-field scenarios.

Abstract

We investigate the primordial trispectra of the general multifield DBI inflationary model. In contrast with the single field model, the entropic modes can source the curvature perturbations on the super horizon scales, so we calculate the contributions from the interaction of four entropic modes mediating one adiabatic mode to the trispectra, at the large transfer limit ($T_{RS}\gg1$). We obtained the general form of the 4-point correlation functions, plotted the shape diagrams in two specific momenta configurations, "equilateral configuration" and "specialized configuration". Our figures showed that we can easily distinguish the two different momenta configurations.

Figures (7)

• Figure 1: Diagrammatic representation of the 3-point vertices: dashed line denotes for the entropic mode $Q_s$,solid line for the adiabatic mode $Q_{\sigma}$, and vertex $a$ presents for the interaction $H^I_3$, vertex $b$ for $H^I_4$, vertex $c$ for $H^I_5$.
• Figure 2: This figure illustrates the interaction between four entropic modes through mediating one adiabatic mode.
• Figure 3: Tetrahedron configuration: momenta $({\bf p}_1,{\bf p}_2,{\bf p}_3,{\bf p}_4)$ do not lie in the same plane, six momenta $(p_1,p_2,p_3,p_4,p_{12},p_{14})$ form a tetrahedron.
• Figure 4: Planar configuration: momenta $({\bf p}_1,{\bf p}_2,{\bf p}_3,{\bf p}_4)$ lie in the same plane, and form a planar quadrangle.
• Figure 5: Shape of the equilateral configuration $\mathcal{A}(p_{12},p_{14})$: in this configuration we set ($p_1=p_2=p_3=p_4=1$).