Numerical Studies Of The Dark Energy Problem

Since the discovery of cosmic acceleration by type la supernovae (SNIa) in1998, dark energy (DE) has become one of the most attracting researching area in modern physics. The origin, properties of DE all remain mysterious, and we are faced with the challenges of the "cosmological constant problems":Why the energy density of DE is so small? Why it is the same order as matter density today? So far, theorists have made great effort to solve the DE problem, with nu-merous models proposed from various aspects, while the DE problem still remains unsolved.Without compelling theoretical explanations for DE, we must turn to ex-periments, in hope that cosmological observations can provide us more clues for the study of DE. Fortunately, cosmologists have developed various observational techniques to probe DE, including the type la supernovae, baryon acoustic oscilla-tions, cosmic microwave background, weak lensing, and so on. These observations further confirmed the cosmic acceleration, and greatly improved the precision of the DE measurement. For future plans, cosmologists are also planning some am-bitious future DE projects like LSST, SKA and so on, in hope to provide more clues about DE through more precise measurements.My Ph. D study focus on the numerical studies of DE. We developed a series of efficient and reliable programmes for cosmological simulations, enabling us to constrain and fit DE models conveniently. Our researching works are as follows:We perform comprehensive studies of the Holographic Dark Energy (HDE), which is proposed by my advisor, Prof. Miao Li. On the theoretical aspect, we proposed the holographic gas model; On the numerical aspect, we perform a series studies of HDE, including the comparison of HDE models with different infrared cut-offs, the constraints on the interaction and curvature in HDE, the generalization of HDE, and the interaction between HDE and dark matter.We also investigated some other DE models. Utilizing the latest observational data, we constrained and compared9DE models and5modified gravity mod-els, and reconstructed the evolution of growth factor in modified gravity models. We investigated a kind of inhomogeneous universe models which can reconstruct the ACDM observations on the past light cone, and proposed to test this model through the cosmic age.We studied the topic of DE reconstruction. By using the redshift-binned and polynomial interpolation parameterizations, we explore the cosmological interpre-tations of the Constitution, Union2and SNLS3supernovae dataset, respectively. Our focuss include the cosmic expansion history, the evolution of the DE equation-of-state and energy density, and so on. We find that the constitution dataset fa-vors dynamical DE, while the Union2and SNLS3dataset favor the cosmological constant.We also investigated some interesting issues related with DE. We made some preliminary investigations of the tension problem between different supernoave dataset. We also investigated the cosmic age problem caused by some old astro-nomical objects. By introducing the DE-dark matter interaction, we find that the cosmic age problem become less sever, although still can not be totally re-solved. Finally, making use of the parametrization method, we also studied the influence of DE on the fate of the universe. We find that, in the worst situation, our universe could exist for16.2Gyr before big rip.