Reheating induced by competing decay modes

We address the problem of studying the decay of the inflaton field phi to another scalar field chi through parametric resonance in the case of a coupling that involves several decay modes. This amounts to the presence of extra harmonic terms in the perturbation of the chi field dynamics. For the case of two frequencies we compute the geometry of the resonance regions, which is significantly altered due to the presence of noncuspidal resonance regions associated to higher harmonics and to the emergence of instability "pockets." We discuss the effect of this change in the efficiency of the energy transfer process for the simplest case of a coupling given by a combination of the two interaction terms of homogeneous degree usually considered in the literature. We find that the presence of higher harmonics has limited cosmological implications.