Equilateral non-Gaussianity from heavy fields

TL;DR

The paper investigates how nonlinear self-interactions of heavy fields during inflation imprint primordial non-Gaussianity, focusing on a constant-turn quasi-single field model. It develops an infrared effective field theory by integrating out the heavy isocurvature mode, yielding a curvature-action with a modified sound speed $\frac{1}{c_s^2} = 1 + \frac{4 \dot\theta_0^2}{m_{\rm eff}^2}$ and a cubic operator sourced by $V'''$, which produces equilateral-type non-Gaussianity. A parallel calculation using the in-in formalism confirms that the heavy-field cubic interaction generates an equilateral bispectrum with $f_{NL}^{\delta\sigma^3} = \frac{40}{243} \frac{R\dot\theta_0^4 c_s^2}{H^6 \mu^6} V'''$, matching the EFT result in the large-mass limit $\mu \gg 1$. The work demonstrates a consistent picture in which hidden heavy sectors can leave sizable equilateral signatures, and it outlines the regime of validity and direction for extending to higher-order correlators and loop effects.

Abstract

The effect of self-interactions of heavy scalar fields during inflation on the primordial non-Gaussianity is studied. We take a specific constant-turn quasi-single field inflation as an example. We derive an effective theory with emphasis on non-linear self-interactions of heavy fields and calculate the corresponding non-Gaussianity, which is of equilateral type and can be as relevant as those computed previously in the literature. We also derive the non-Gaussianity by directly using the in-in formalism, and verify the equivalence of these two approaches.

Figures (1)

• Figure 1: A schematic diagram that shows how the self-interaction of the heavy field $\delta\sigma$ affects the three-point function of the light field $\delta\theta$. The contribution of the cubic interaction $V"'\delta\sigma^3/6$ is transferred to three $\delta\theta$'s by the quadratic interaction $2R\dot\theta_0\dot{\delta\theta}\delta\sigma$.