Influence of heavy modes on perturbations in multiple field inflation

TL;DR

The paper addresses how heavy field directions modify linear perturbations in multi-field inflation and when a low-energy EFT based on a single light mode suffices. By adopting a mass basis and integrating out heavy modes, it derives a multi-dimensional effective action for light modes with a propagation matrix that generalizes the single-field sound speed. It then analyzes sudden turns in field space, showing that soft turns preserve EFT validity while sharp turns excite heavy modes, imprinting oscillatory signatures in the power spectrum and, in some regimes, requiring the full two-field description. A detailed comparison between the mass-basis EFT, a traditional adiabatic-entropic basis, and a concrete two-field model confirms the predicted light- and heavy-mode contributions and highlights the conditions under which heavy modes leave observable imprints. The results provide a framework for incorporating heavy degrees of freedom in inflationary perturbations and motivate further exploration of non-Gaussianities and non-canonical kinetic terms.

Abstract

We investigate linear cosmological perturbations in multiple field inflationary models where some of the directions are light while others are heavy (with respect to the Hubble parameter). By integrating out the massive degrees of freedom, we determine the multi-dimensional effective theory for the light degrees of freedom and give explicitly the propagation matrix that replaces the effective sound speed of the one-dimensional case. We then examine in detail the consequences of a sudden turn along the inflationary trajectory, in particular the possible breakdown of the low energy effective theory in case the heavy modes are excited. Resorting to a new basis in field space, instead of the usual adiabatic/entropic basis, we study the evolution of the perturbations during the turn. In particular, we compute the power spectrum and compare with the result obtained from the low energy effective theory.

Figures (14)

• Figure 1: Schematic representation of the background trajectory in field space during a single turn. The dashed line represents the light direction of the potential (i.e. the bottom of the valley). If the turn is "soft", the trajectory deviates slightly from the bottom and remains smooth (blue line). If the turn is sharp, the trajectory deviates from the light valley significantly and oscillates after the turn (red line).
• Figure 2: Evolution of the angle $\psi$ during a sharp turn as a function of the number of e-folds, for various values of $\mu/\omega$ (and $m_h/H=10$). The colored continuous lines correspond to the numerical integration of Eq.(\ref{['theta_2nd_eom_2f']}) with constant $H$, while the black dashed lines are obtained from the analytical approximation Eq.(\ref{['psi_sharp_app']}).
• Figure 3: Evolution of $\psi$ during a soft turn (for $m_h/H=10$). The colored lines correspond to the numerical integration of Eq.(\ref{['theta_2nd_eom_2f']}) with constant $H$, while the black dashed lines are given by the analytical approximation Eq.(\ref{['psi_soft_app']}).
• Figure 4: Contour plot of the valley corresponding to the potential Eq. (\ref{['func_potential']}), with the numerical parameters given in Eq. (\ref{['parameter_set']}).
• Figure 5: Background trajectories around the turn for different values of the sharpness parameter $s$. The field $\phi$ increases with time.