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Title: Late-Time Acceleration in Bouncing Cosmologies
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Abstract: In this talk, we are going to revisit some nonsingular cosmological models in the framework
of modified gravity which can be constrained by observational data. All the models are sourced with
the most appealing candidate for dark energy, namely, a cosmological constant.
The simplest model refers to a Friedmann geometry plus noninteracting perfect fluids together with a conformally coupled scalar field. It can be shown that in narrow windows of the parameter space, labelled by an integer $n\geq2$, nonlinear resonance phenomena may destroy the KAM tori that trap the scalar field, leading to an exit to late-time acceleration. To proceed we consider a more general case feeding the metric with a Bianchi IX geometry. It can be shown that a saddle-centre-centre engenders in the phase space the topology of stable and unstable 4-dim cylinders. For the stable and unstable cylinders we have the oscillatory motion about the separatrix towards the bounce which may lead to homoclinic transversal intersection of the cylinders. This behaviour defines a chaotic saddle which allows one to obtain late-time acceleration due to an invariant signature of chaos in the model.