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

TL;DR

This paper investigates how nonlinear resonance phenomena in Hořava-Lifshitz bouncing cosmologies influence the universe's evolution, potentially leading to accelerated expansion by breaking phase space tori and constraining model parameters.

Contribution

It introduces the analysis of nonlinear resonance effects in Hořava-Lifshitz bouncing cosmologies and their role in enabling accelerated expansion.

Findings

Nonlinear resonance can destroy KAM tori in phase space.

Resonance phenomena impose constraints on model parameters.

Resonance can lead to exit from bouncing phase to de Sitter attractor.

Abstract

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.