含曲率效應之阮道-桑卓姆型膜宇宙學：早期及晚期宇宙

Abstract

The brane-world scenario provides an intriguing possibility to explore the phenomenological cosmology implied by string/M theory. Among several developments within this field, we consider a modified Randall-Sundrum single brane model with two natural generalizations: a Gauss-Bonnet term in the five-dimensional bulk action as well as an induced gravity term in the four-dimensional brane action, which are the leading-order corrections to the Randall-Sundrum model. In this thesis, we will look into the cosmological and theoretical aspects of the model and explore in particular its phenomenological implications in the early and late evolution of the Universe. In the early Universe, we are mainly interested in the primordial inflationary era of the brane, where the background, with a single inflaton field confined to the brane, is modeled through a quasi-de Sitter brane embedded in an anti-de Sitter bulk. In this framework, we study the influence of these combined curvature effects on the primordial scalar and tensor perturbations generated during an extreme slow-roll inflationary epoch on the brane. As a result, we show that both curvature effects at high energies tend to suppress the enhancement of the amplitude of these cosmological perturbations in the Randall-Sundrum model. Moreover, the GB effect, as compared with standard general relativity, will abruptly enhance the tensor-to-scalar ratio and break the standard consistency relation at high energies, which can not be avoided by invoking the induced gravity effect. In the late Universe, we investigate the ultimate fate of the brane Universe filled with a phantom dark energy. In standard general relativity, there exist dark energy models that predict the occurrence of a “little rip” event, which is quite similar to the big rip singularity except that the former happens in the infinite future while the latter at a finite cosmic time; for an expanding Universe, both events happen in the future and at high energies. Therefore, we wonder whether this little rip event can be smoothed in some way by considering the ultra-violet and infra-red modifications to general relativity codified on these curvature effects in the Randall-Sundrum model. It turns out that the little rip event is transformed into a sudden singularity in this scenario. Finally, from the theoretical perspective, we look into the ghost problem in the self-accelerating branch of this model. The Dvali-Gabadadze-Porrati brane-world model provides a possible approach to address the late-time cosmic acceleration. However, it has subsequently been pointed out that a ghost instability will arise on its self-accelerating branch. Here, we carefully investigate whether this ghost problem could possibly be cured by introducing the Gauss-Bonnet term in the five-dimensional bulk action. Our result shows that the ghost excitations are still present even in this modified model. This thesis is based on our publications [1-4]. In addition, during the same period we published [5], whose content is not included in the present manuscript. Moreover, we published as well two refereed proceedings [6,7].