On reaching the adiabatic limit in multi-field inflation

TL;DR

This paper investigates the predictions of two-field no-scale inflation models in supergravity, emphasizing the importance of curvature-isocurvature coupling and the conditions for reaching the adiabatic limit to produce reliable cosmological observables.

Contribution

It provides a detailed analysis of the coupling effects in multi-field inflation and identifies universal geometrical contributions affecting the predictions of inflationary models.

Findings

Coupling between curvature and isocurvature perturbations significantly affects $n_s$ and $r$.

Universal geometrical contribution influences the effective isocurvature mass.

Spectator fields can cause oscillatory features in power spectra at inflation's end.

Abstract

We calculate the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ in a class of recently proposed two-field no-scale inflationary models in supergravity. We show that, in order to obtain correct predictions, it is crucial to take into account the coupling between the curvature and the isocurvature perturbations induced by the noncanonical form of the kinetic terms. This coupling enhances the curvature perturbation and suppresses the resulting tensor-to-scalar ratio to the per mille level even for values of the slow-roll parameter $\epsilon \sim 0.01$. Beyond these particular models, we emphasise that multifield models of inflation are a priori not predictive, unless one supplies a prescription for the post-inflationary era, or an adiabatic limit is reached before the end of inflation. We examine the conditions that enabled us to actually derive predictions in the models under study, by analysing the various contributions to the effective isocurvature mass in general two-field inflationary models. In particular, we point out a universal geometrical contribution that is important at the end of inflation, and which can be directly extracted from the inflationary Lagrangian, independently of a specific trajectory. Eventually, we point out that spectator fields can lead to oscillatory features in the time-dependent power spectra at the end of inflation. We demonstrate how these features can be model semi-analytically as well as the theoretical uncertainties they can entail.