Effective Field Theory and Decoupling in Multi-field Inflation: An Illustrative Case Study

Abstract

We explore the effects of heavy degrees of freedom on the evolution and perturbations of light modes in multifield inflation. We use a simple two-field model as an example to illustrate the subtleties of integrating out massive fields in a time-dependent background. We show that when adiabaticity is violated due to a sharp turn in field space, the roles of massive and massless field are interchanged, and furthermore the fields are strongly coupled; thus the system cannot be described by an effective single field action. Further analysis shows that the sharp turn imparts a non Bunch-Davis component in each perturbation mode, leading to oscillatory features in the power spectrum, and a large resonantly enhanced bispectrum.

Figures (1)

• Figure 2: Illustration of a sharp turn in field space. The green dashed line represents the massless field (inflaton) direction, and the massive field is orthogonal to the green dashed line. Along the blue part of the trajectory, the kinetic energy of the inflaton is gradually transformed into the potential energy of the massive field. At the end of the blue line, the potential enegry starts to convert back to the kinetic energy, and caused subsequent oscillations of the massive field along the transverse direction (red curve). The perturbations in the massive field are projected into the inflaton direction at the interface between the blue and red curve, and this is the effect we focus on in this paper. The turning angle shown in this figure is made very large to illustrate the excitation of massive modes. In reality, a much smaller turning angle is sufficient, and we will show that $\Delta \theta \lesssim 0.1$ from constraints on the power spectrum.