We examine the dynamics of scalar perturbations in closed Friedmann-Lemaître-Robertson-Walker universes in the framework of brane world theory with a timelike extra dimension. In this scenario, the unperturbed Friedmann equations contain additional terms arising from the bulk-brane interaction that implement nonsingular bounces in the models with a cosmological constant and noninteracting perfect fluids. The structure of the phase space of the models allows for two basic configurations, namely, one bounce solutions and eternal universes. Assuming that the matter content of the model is given by dust and radiation, we derive the dynamical field equations for scalar hydrodynamical perturbations considering either a conformally flat (de Sitter) bulk or a perturbed bulk. The dynamical system built with these equations is extremely involved. Nevertheless, in this paper we perform a numerical analysis which can shed some light on the study of cosmological scalar perturbations in bouncing brane world models. From a mathematical point of view we show that although the bounce enhances the amplitudes of scalar perturbations for one bounce models in the case of a de Sitter bulk, the amplitudes of the perturbations remain sufficiently small and bounded relative to the background values up to a certain scale. For one bounce models in the case of a perturbed bulk the amplitudes of all perturbations (apart from the Weyl fluid energy density) remain sufficiently small and bounded relative to the background values for any scale of the perturbations. We also discuss and compare the stability and bounded behavior of the perturbations in the late accelerated phase of one bounce solutions. For eternal universes we argue that some of these features are maintained only for early times (typically of the order of the first bounce). In this sense we show that eternal solutions are highly unstable configurations considering the background model of this paper. © 2013 American Physical Society.
Bounded scalar perturbations in bouncing brane world cosmologies
Pace F.;
2013-01-01
Abstract
We examine the dynamics of scalar perturbations in closed Friedmann-Lemaître-Robertson-Walker universes in the framework of brane world theory with a timelike extra dimension. In this scenario, the unperturbed Friedmann equations contain additional terms arising from the bulk-brane interaction that implement nonsingular bounces in the models with a cosmological constant and noninteracting perfect fluids. The structure of the phase space of the models allows for two basic configurations, namely, one bounce solutions and eternal universes. Assuming that the matter content of the model is given by dust and radiation, we derive the dynamical field equations for scalar hydrodynamical perturbations considering either a conformally flat (de Sitter) bulk or a perturbed bulk. The dynamical system built with these equations is extremely involved. Nevertheless, in this paper we perform a numerical analysis which can shed some light on the study of cosmological scalar perturbations in bouncing brane world models. From a mathematical point of view we show that although the bounce enhances the amplitudes of scalar perturbations for one bounce models in the case of a de Sitter bulk, the amplitudes of the perturbations remain sufficiently small and bounded relative to the background values up to a certain scale. For one bounce models in the case of a perturbed bulk the amplitudes of all perturbations (apart from the Weyl fluid energy density) remain sufficiently small and bounded relative to the background values for any scale of the perturbations. We also discuss and compare the stability and bounded behavior of the perturbations in the late accelerated phase of one bounce solutions. For eternal universes we argue that some of these features are maintained only for early times (typically of the order of the first bounce). In this sense we show that eternal solutions are highly unstable configurations considering the background model of this paper. © 2013 American Physical Society.
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