We study models of inflation with two scalar fields and non-canonical kinetic terms, focusing on the case in which the curvature and isocurvature perturbations are strongly coupled to each other. In the regime where a heavy mode can be identified and integrated out, we clarify the passage from the full two-field model to an effectively single-field description. However, the strong coupling sets a new scale in the system, and affects the evolution of the perturbations as well as the beginning of the regime of validity of the effective field theory. In particular, the predictions of the model are sensitive to the relative hierarchy between the coupling and the mass of the heavy mode. As a result, observables are not given unambiguously in terms of the parameters of an effectively single field model with non-trivial sound speed. Finally, the requirement that the sound horizon crossing occurs within the regime of validity of the effective theory leads to a lower bound on the sound speed. Our analysis is done in an extremely simple toy model of slow-roll inflation, which is chosen for its tractability, but is non-trivial enough to illustrate the richness of the dynamics in non-canonical multi-field models.
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