Nonlinear resonance is ubiquitous in nature. Resonance is relevant to understanding phenomena in quite distinct areas such as music, cellular structure, and astrophysics, and in the very early universe. In order to see the crucial role played by resonance in cosmology, we assume that closed FRW universes with a massive inflaton field evolve according to the field equations that contain additional terms arising from high energy corrections to cosmological scenarios. As a consequence, nonsingular bounces in the early evolution of the universe are produced. We have shown that in narrow windows of the parameter space of the models, nonlinear resonance phenomena of KAM tori occur and lead to the destruction of those tori that trap the inflaton, resulting in the escape of the universe into inflation. These resonance windows are labeled by an integer n ≥ 2; n is related to the ratio of the frequencies in the scale factor/scalar field degrees of freedom.
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