Adiabatic and isocurvature perturbations in extended theories with kinetic couplings

The scalar field sector in low--energy effective field theories motivated by string theory often contains several scalar fields, some of which possess non--standard kinetic terms. In this paper, we study theories with two scalar fields, in which one of the fields has a non--canonical kinetic term. The kinetic coupling is allowed to depend on both fields, going beyond the work in the literature, which usually considers the case of the coupling to depend on the other field only. Our aim is to study adiabatic and isocurvature perturbations in these extended theories. Our results show that the evolution equation for the curvature perturbation does not change when allowing the coupling to depend on both fields, while the effective mass of the entropy perturbation changes. We find expressions for the spectral index and its running at horizon crossing and at the end of inflation. We apply the formalism and study three phenomenological models, with different kinetic couplings.