Some Numerical Studies On Cosmic Acceleration

This thesis introduces the numerical studies on a series of issues about the cosmic acceleration. Our research area covers all aspects of the cosmic acceleration research, including dark energy, modified gravity and inhomogeneous universe.We discuss three dark energy models based on the holographic principle:the holographic dark energy, the agegraphic dark energy, and the holographic Ricci dark energy. Although these three models have been studied widely, no compar-ison of them has been made in the previous literature. We constrain these three models by using the type la supernovae, the cosmic microwave background, and the baryon acoustic oscillations data, then compare them utilizing the Bayesian evidence. It is shown that among these three models, the holographic dark en-ergy model is most favored by the observational data. In addition, by using the same data, we further probe interaction and spatial curvature in the holographic dark energy model. It is found that, although there exists significant degeneracy between the interaction and the spatial curvature, the original holographic dark energy model with zero interaction and flat geometry is still favored by cosmolog-ical observations.We introduce three dark energy reconstruction methods:specific ansatz, binned parametrization, and polynomial fitting. For each reconstruction method, we describe the basic idea, and introduce some most popular models as examples. We also propose a new reconstruction form, which is a binned parametrization treating the discontinuity points of redshift as free parameters. Utilizing these re-construction methods, we study three supernovae datasets:Constitution, Union2and SNLS3. During the process of analysis, we mainly focus on our new recon-struction method. It is found that the Constitution dataset favors a dynamical dark energy, while both the Union2and the SNLS3dataset favor a cosmological constant.We investigate the cosmic age problem associated with nine extremely old globular clusters and one very old high-redshift quasar. We find that, if the age estimates of these objects are correct, the cosmic age puzzle still remains in the cosmological constant model. After demonstrating that the high-redshift cosmic age problem can not be solved by any non-interaction model, we also study three interacting dark energy models. It is shown that, although the introduction of interaction can give a larger cosmic age, the interacting dark energy models still have difficulty to pass the cosmic age test. In addition, under the framework of dynamical dark energy, we explore the ultimate fate of the Universe. It is found that, at the2σ confidence level, our Universe can still exist at least16.7Gyr. We also discuss, if the doomsday exists, when would the gravitationally bound systems be destroyed. A simple analytical formula is obtained.By using the current type la supernovae, cosmic microwave background, bary-on acoustic oscillations and Hubble constant data, we study five modified gravity models, including the DGP model, two f(T) models, and two f(R) models. It is shown that, the DGP model is ruled out by cosmological observations, and other modified gravity models are also not as good as the cosmological constant model. In addition, based on the data fitting result, we also study the the evolutions of the growth factor in these models. Comparing with the result of the cosmological constant model, We find that the current growth factor data are not enough to distinguish these modified gravity models from the cosmological constant model.We study an inhomogeneous Universe model, which exactly reconstruct the cosmological constant model on the past light-cone. Since this model has the same luminosity-distance and mass density with the cosmological constant model, it is very difficult to distinguish it from the cosmological constant model. We demonstrate that the age of the universe is a good touchstone, which can be used to distinguish them. Utilizing the cosmological constraints given by the WMAP7-year observations, we find that the1σ upper limit of the cosmic age given by this inhomogeneous Universe model is t<11.7Gyr, which is about2Gyr smaller than the result of the cosmological constant model. Since the current Milky Way observations have already given a lower limit on the age of the Universe of about11.2Gyr, future observations on the ages of old objets may distinguish these two models.