Non-linear curvature perturbation in multi-field inflation models with non-minimal coupling

TL;DR

This paper investigates non-linear curvature perturbations in multi-field inflation with non-minimal coupling, analyzing differences between Jordan and Einstein frames, and provides examples consistent with recent Planck observations.

Contribution

It derives relations for curvature perturbations in different frames and explores their implications in specific non-minimally coupled inflation models.

Findings

Predictions can match Planck data with small tensor-to-scalar ratio and suppressed non-Gaussianity.

Non-minimal coupling can significantly alter inflationary parameter predictions.

Spectral tilt constraints can limit non-minimal coupling parameters.

Abstract

Using the \delta N formalism we consider the non-linear curvature perturbation in multi-field models of inflation with non-minimal coupling. In particular, we focus on the relation between the \delta N formalism as applied in the conformally related Jordan and Einstein frames. Exploiting results already known in the Einstein frame, we give expressions for the power spectrum, spectral tilt and non-gaussianity associated with the Jordan frame curvature perturbation. In the case that an adiabatic limit has not been reached, we find that in general these quantities differ from those associated with the Einstein frame curvature perturbation, and also confirm their equivalence in the absence of isocurvature modes. We then proceed to consider two analytically soluble examples, the first involving a non-minimally coupled `spectator' field and the second being a non-minimally coupled extension of the multi-brid inflation model. In the first model we find that predictions can easily be brought into agreement with the recent Planck results, as the tensor-to-scalar ratio is generally small, the spectral tilt tuneable and the non-gaussianity suppressed. In the second model we find that predictions for all three parameters can differ substantially from those predicted in the minimally coupled case, and that the recent Planck results for the spectral tilt can be used to constrain the non-minimal coupling parameters.