Nonlinear Resonance in Ho\v{r}ava-Lifshitz Bouncing Cosmologies

In this paper I examine the phase space dynamics in the framework of Non-Projectable Ho\v{r}ava-Lifshitz bouncing cosmologies. By considering a closed Friedmann-Lema\^itre-Robertson-Walker (FLRW) geometry, the first integral contains a correction term that leads to nonsingular metastable bounces in the early evolution of the universe. The matter content of the model is a massive conformally coupled scalar field, dust and radiation. A nonvanishing cosmological constant connected to a de Sitter attractor in the phase space is also assumed. In narrow windows of the parameter space, labeled by an integer $n\geq 2$, nonlinear resonance phenomena may destroy the KAM tori that trap the scalar field, leading to an exit to the de Sitter attractor. As a consequence nonlinear resonance imposes constraints on the parameters and in the initial configurations of the models so that an accelerated expansion may be realized.