Cosmological perturbation theory with trinity of scalar fields

Abstract

We present an explicit formulation of cosmological perturbation theory for three-field models with a flat field space. By performing rotations to align one field with the direction of curvature perturbations and applying the same rotations to the other two field directions, we introduce the semikinematic basis, which is applicable to models with more than two fields. We derive the governing equations in this basis. We also stress a characteristic property of more-than-two-field models: the freedom in choosing the isocurvature perturbations. This framework enables the computation of the curvature and two isocurvature power spectra for any given potential. We numerically solve the background and perturbation equations for three distinct scenarios. First, to validate the consistency of our three-field formalism, we examine an effective two-field model inspired by the two-block case of the multigiant vacua matrix inflation scenario. Next, we analyze a purely three-field system without direct interfield interactions. Finally, we study a three-field case that incorporates direct interactions. For all scenarios, we numerically compute the curvature perturbation power spectra and highlight the effects of rapid turns on the spectra. Finally, we investigate the relationship between these quantities and the observables in the early radiation-dominated era. Through both general arguments and a simple example, we show that three-field inflation can yield a much richer phenomenology. This is particularly true when we assume the initial perturbations in the radiation era include two isocurvature modes.