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

Abstract

Using the δN formalism we consider the non-linear curvatureperturbation in multi-field models of inflation with non-minimalcoupling. In particular, we focus on the relation between the δN formalism as applied in the conformally related Jordan and Einsteinframes. Exploiting results already known in the Einstein frame, wegive 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 thatin general these quantities differ from those associated with theEinstein frame curvature perturbation, and also confirm theirequivalence in the absence of isocurvature modes. We then proceed toconsider two analytically soluble examples, the first involving anon-minimally coupled `spectator' field and the second being anon-minimally coupled extension of the multi-brid inflation model. Inthe first model we find that predictions can easily be brought intoagreement with the recent Planck results, as the tensor-to-scalarratio is generally small, the spectral tilt tuneable and the non-gaussianitysuppressed. In the second model we find that predictions for all threeparameters can differ substantially from those predicted in theminimally coupled case, and that the recent Planck results forthe spectral tilt can be used to constrain the non-minimal couplingparameters.