Adiabatic and isocurvature perturbations for multifield generalized Einstein models

Low energy effective field theories motivated by string theory will likely contain several scalar moduli fields which will be relevant to early Universe cosmology. Some of these fields are expected to couple with nonstandard kinetic terms to other fields. In this paper, we study the splitting into adiabatic and isocurvature perturbations for a model with two scalar fields, one of which has a nonstandard kinetic term in the Einstein-frame action. Such actions can arise, e.g., in the pre-big-bang and ekpyrotic scenarios. The presence of a coupling through a nonstandard kinetic term induces a novel coupling between adiabatic and isocurvature perturbations which is nonvanishing when the potential for the matter fields is nonzero. This coupling is unsuppressed in the long wavelength limit and thus can lead to an important transfer of power from the entropy to the adiabatic mode on super-Hubble scales. We apply the formalism to the case of a previously found exact solution with an exponential potential and study the resulting mixing of adiabatic and isocurvature fluctuations in this example. We also discuss the possible relevance of the extra coupling in the perturbation equations for the process of generating an adiabatic component of the fluctuation spectrum from isocurvature perturbations without considering a later decay of the isocurvature component.