Slow-roll suppression of adiabatic instabilities in coupled scalar field-dark matter models

We study the evolution of linear density perturbations in the context of interacting scalar field-dark matter cosmologies, where the presence of the coupling acts as a stabilization mechanism for the runaway behavior of the scalar self-interaction potential as in the case of the chameleon model. We show that, in the ``adiabatic'' background regime of the system, the rise of unstable growing modes of the perturbations is suppressed by the slow-roll dynamics of the field. Furthermore, the coupled system behaves as an inhomogeneous adiabatic fluid. In contrast, instabilities may develop for large values of the coupling constant, or along nonadiabatic solutions, characterized by a period of high-frequency dumped oscillations of the scalar field. In the latter case, the dynamical instabilities of the field fluctuations, which are typical of oscillatory scalar field regimes, are amplified and transmitted by the coupling to dark matter perturbations.