Large non-Gaussianities in the Effective Field Theory Approach to Single-Field Inflation: the Trispectrum

TL;DR

The paper develops a comprehensive EFT of single-field inflation up to fourth order to study the trispectrum, using curvature-generated operators and two approximate symmetries to organize the operator content. Employing the IN-IN formalism, it separates scalar-exchange and contact-interaction contributions and analyzes trispectrum shapes across multiple configurations, revealing distinctive features from curvature terms such as those controlled by ${ar M}_6$ that can yield large signals. Key findings include large trispectrum amplitudes from symmetry-allowed curvature-generated operators, novel shape-function patterns that differ from DBI/Ghost-inflation templates, and a demonstration that double-squeezed configurations do not trivially distinguish third- versus fourth-order contributions. The work reinforces the utility of EFT and symmetry considerations in constraining inflationary models and informing observational trispectrum searches with Planck and related data.

Abstract

We perform the analysis of the trispectrum of curvature perturbations generated by the interactions characterizing a general theory of single-field inflation obtained by effective field theory methods. We find that curvature-generated interaction terms, which can in general give an important contribution to the amplitude of the four-point function, show some new distinctive features in the form of their trispectrum shape-function. These interesting interactions are invariant under some recently proposed symmetries of the general theory and, as shown explicitly, do allow for a large value of the trispectrum.

Figures (13)

• Figure 1: The equilateral configuration shape is presented on the left from the scalar exchange contribution of the $\bar{M}_6$-driven interaction. The shape-function is different from the plots presented in chen-tris. On the other hand, once a necessary change of variables has been performed, it is qualitatively similar to the shape for the contact interaction diagram which arises from the ghost inflation $(\nabla \pi)^4$ interaction term in muko. On the right we plotted our findings for the $\bar{M}_6$-generated interaction in the folded configuration. It very much resembles the ones obtained in chen-tris for the scalar exchange diagrams from DBI-like terms, especially from the interaction $\dot \pi (\nabla \pi)^2$ . In all the pictures above and below $k_1$ has ben set equal to unity without loss of generality.
• Figure 2: On the left the plot obtained for the $\bar{M}_6$ interaction in the planar configuration plot. Note here some of the interesting features: as $k_2,k_4 \rightarrow 0$ the shape function goes to zero, much like it happens for DBI-generated interactions. As $k_2,k_4 \rightarrow 2$ the shape function reaches values that are negative, albeit slightly so. Looking at the $k_2 = k_4$ line we see that it is convex, rather than concave as found for other interaction types in chen-tris On the right the planar limit double squeezed configuration is plotted. In the region of interest, namely for $k_{12} \rightarrow 0$, the shape function is non-zero, finite and negative; this again is different than what found in chen-tris for a variety of DBI-originated terms.
• Figure 3: The equilateral configuration shape for the ${\cal O}_{1}$ operator is presented on the left. It is different from the results in chen-tris and very much resembles the plot we obtained for the scalar exchange calculation. Notice that upon performing a change of variables, it is basically identical to the $(\nabla \pi)^4$ interaction term plotted in muko (We elaborate further on this point in Appendix B). On the right we plotted our findings for the ${\cal O}_{1}$ interaction term in the folded configuration. As it will be for the other interactions, this configurations provides no particularly distinctive features that would allow to single out the constributions from the different interaction operators.
• Figure 4: The ${\cal O}_{1}$ interaction planar configuration shape on the left is not exceedingly different from the ones presented in chen-tris: it vanishes for $k_2, k_4 \rightarrow 0$, it is peaked for $k_2 = 2 = k_4$. On the $k_2=k_4$ line the shapefunction is convex, rather than concave as for the contact interaction term plotted in chen-tris. On the right we plotted the ${\cal O}_{1}$ interaction shape function in the planar limit double squeezed configuration. Here we immediately note an interesting feature: despite this being a contribution to the contact interaction diagram, in the $k_4=k_{12} \rightarrow 0$ it gives a finite, non zero shape function. We comment more on this fact in the text.
• Figure 5: The equilateral configuration shape is presented on the left for the ${\cal O}_{2}$ operator. Because of the way the space derivatives are written in Fourier space there's no $k_{12}, k_{14}$ dependence and so one gets a plateau. On the right our findings for ${\cal O}_{2}$ in the folded configuration.