Combined local and equilateral non-Gaussianities from multifield DBI inflation

TL;DR

This paper investigates multifield DBI inflation where curvature perturbations arise from entropy fluctuations converted into adiabatic perturbations at the end of brane inflation. It combines the delta-N formalism with a two-field DBI setup to derive the power spectrum, bispectrum, and trispectrum, showing that entropy-to-curvature transfer enhances the curvature perturbations and yields both local and equilateral non-Gaussianities, with a distinctive trispectrum component proportional to $f_{NL}^{\rm loc} f_{NL}^{\rm eq}$. The authors derive explicit expressions for the transfer parameter $T_{\sigma s}$, the running of non-Gaussianities, and observational constraints (e.g., $\beta \lesssim 0.1$) arising from Planck/WMAP bounds, highlighting how trispectrum measurements can break degeneracies between multifield and single-field DBI scenarios. The results provide a structural, model-independent signature of multifield DBI inflation and point to the trispectrum as a powerful discriminator for end-of-inflation modulation mechanisms in string-inspired cosmologies.

Abstract

We study multifield aspects of Dirac-Born-Infeld (DBI) inflation. More specifically, we consider an inflationary phase driven by the radial motion of a D-brane in a conical throat and determine how the D-brane fluctuations in the angular directions can be converted into curvature perturbations when the tachyonic instability arises at the end of inflation. The simultaneous presence of multiple fields and non-standard kinetic terms gives both local and equilateral shapes for non-Gaussianities in the bispectrum. We also study the trispectrum, pointing out that it acquires a particular momentum dependent component whose amplitude is given by $f_{NL}^{loc} f_{NL}^{eq}$. We show that this relation is valid in every multifield DBI model, in particular for any brane trajectory, and thus constitutes an interesting observational signature of such scenarios.

Figures (5)

• Figure 1: A simplified picture of the geometry at the tip of the throat, with one angular direction $\theta$ only. The radial inflationary trajectory is represented by the blue line.
• Figure 2: The tachyon surface, at which inflation ends, in the $\phi-\theta$ plane. The end value of the inflaton is shifted from ${\overline \phi_e}$ to ${\overline \phi_e} +\delta \phi_e$ due to the angular fluctuation $Q_{\theta}$, hence the duration of inflation varies from one super-Hubble region to another.
• Figure 3: In this group of figures, we consider the equilateral limit $k_1=k_2=k_3=k_4$, and plot $T_{loc,\;eq}$, $T_{loc1}$ and $T_{loc2}$, respectively, as functions of $k_{12}/k_1$ and $k_{14}/k_1$. Note that $T_{loc,\;eq}$ and $T_{loc1}$ blow up when $k_{12}\ll k_1$ and $k_{14} \ll k_1$, as well as in the other boundary, corresponding to $k_{13}\ll k_1$.
• Figure 4: In this group of figures, we consider the specialized planar limit with $k_1=k_3=k_{14}$, and plot $T_{loc,\;eq}$, $T_{loc1}$ and $T_{loc2}$, respectively, as functions of $k_{2}/k_1$ and $k_{4}/k_1$. Along the diagonal $k_2 \rightarrow k_4$, $T_{loc,\;eq}$ and $T_{loc1}$ blow up because in this limit, $k_{13}\rightarrow 0$. At the $k_2\rightarrow 0$ and $k_4\rightarrow 0$ boundaries, $T_{loc,\;eq}$ blow up while the local shapes remain finite. Notice that the sign of $T_{loc,\;eq}$ varies non trivially over the parameter space.
• Figure 5: In this group of figures, we look at the shapes near the double squeezed limit: we consider the case where ${k}_3={k}_4=k_{12}$ and the tetrahedron is a planar quadrangle. We plot $T_{loc,\;eq}$, $T_{loc1}$ and $T_{loc2}$, respectively, as functions of $k_{4}/k_1$ and $k_{14}/k_1$. Notice that the sign of $T_{loc,\;eq}$ varies non trivially over the domain. In the squeezed limit, at $(k_4/k_1=1,k_{14}/k_1=1)$ where $k_2\to 0$, and in the double-squeezed limit, $k_3=k_4\rightarrow 0$, $T_{loc,\;eq}$ blows up while the local shapes are finite (see the main text for additional comments).