Curvature perturbation in multi-field inflation with non-minimal coupling

TL;DR

This paper investigates how curvature perturbations behave in multi-field inflation models with non-minimal coupling, revealing that their invariance under conformal transformations is broken and that observable predictions depend on the frame used.

Contribution

It demonstrates that curvature perturbations differ between Jordan and Einstein frames in multi-field inflation, emphasizing the non-invariance of adiabaticity under conformal transformations.

Findings

Curvature perturbations are frame-dependent in multi-field models.

Isocurvature perturbations source curvature perturbations across frames.

Conservation of curvature perturbation is frame-specific and not guaranteed.

Abstract

In this paper we discuss a multi-field model of inflation in which generally all fields are non-minimally coupled to the Ricci scalar and have non-canonical kinetic terms. The background evolution and first-order perturbations for the model are evaluated in both the Jordan and Einstein frames, and the respective curvature perturbations compared. We confirm that they are indeed not the same - unlike in the single-field case - and also that the difference is a direct consequence of the isocurvature perturbations inherent to multi-field models. This result leads us to conclude that the notion of adiabaticity is not invariant under conformal transformations. Using a two-field example we show that even if in one frame the evolution is adiabatic, meaning that the curvature perturbation is conserved on super-horizon scales, in general in the other frame isocurvature perturbations continue to source the curvature perturbation. We also find that it is possible to realise a particular model in which curvature perturbations in both frames are conserved but with each being of different magnitude. These examples highlight that the curvature perturbation itself, despite being gauge-invariant, does not correspond directly to an observable. The non-equivalence of the two curvature perturbations would also be important when considering the addition of Standard Model matter into the system.