On the importance of heavy fields during inflation

TL;DR

This work analyzes two-field inflation with a heavy-field mass hierarchy and shows that integrating out the heavy mode yields a reliable EFT for curvature perturbations if the turn rate evolves slowly relative to the heavy mass. The key adiabaticity condition ensures the EFT captures the essential physics of turning trajectories, including large, sharp turns that imprint features in the power spectrum through a reduced and time-varying speed of sound. The authors validate the EFT against full two-field computations across canonical and metric-induced turns, demonstrating when they agree and how features emerge in P_R. The results challenge previous claims about EFT validity and highlight the potential observability of UV-physics signatures in the primordial spectrum even within linear perturbation theory.

Abstract

We study the dynamics of two-field models of inflation characterized by a hierarchy of masses between curvature and isocurvature modes. When the hierarchy is large, a low energy effective field theory (EFT) exists in which only curvature modes participate in the dynamics of perturbations. In this EFT heavy fields continue to have a significant role in the low energy dynamics, as their interaction with curvature modes reduces their speed of sound whenever the multi-field trajectory is subject to a sharp turn in target space. Here we analyze under which general conditions this EFT remains a reliable description for the linear evolution of curvature modes. We find that the main condition consists on demanding that the rate of change of the turn's angular velocity stays suppressed with respect to the masses of heavy modes. This adiabaticity condition allows the EFT to accurately describe a large variety of situations in which the multi-field trajectory is subject to sharp turns. To test this, we analyze several models with turns and show that, indeed, the power spectra obtained for both the original two-field theory and its single-field EFT are identical when the adiabaticity condition is satisfied. In particular, when turns are sharp and sudden, they are found to generate large features in the power spectrum, accurately reproduced by the EFT.

Figures (10)

• Figure 1: The figure illustrates a prototype example of a multi-field potential (depending on two fields $\chi$ and $\psi$) with a mass hierarchy in which the flat direction is subject to a turn.
• Figure 2: Relative orientation of the vector fields $T^a$ and $N^a$ defined with respect to the background solution $\phi_0^a(t)$.
• Figure 3: The $u$-fields represent fluctuations with respect to a fixed local frame, whereas the $v$-fields represent fluctuations with respect to the path (parallel and normal).
• Figure 4: Examples of turns according to the relative size of $\Delta \phi$ and $\kappa$. In the case $\kappa \ll \Delta \phi$ the target space requires a non trivial topology.
• Figure 5: The figure illustrates the case of a turn for which the adiabatic condition $T_{M} \ll T_{\perp}$ is respected. In this case the turn happens adiabaticaly, in the sense that the timescale $T_M$ plays no role during the turn. If $\Delta h / \kappa \sim 1$ the displacement from the flat minima is large and the speed of sound will be reduced considerably.