Models Of Dynamical Dark Energy

The proposing of inflation theory in the early 1980s suggested the birth of particle cosmology, while the discovery of dark energy in 1998 has made it one of the hottest research areas in physics. On the other hand, various experiments in cosmology since the early 1990s, including COBE and WMAP, have measured cosmological parameters to high precision and been found to be in good agreement with cosmological theories like inflation, pronouncing the coming of the era of precision cosmology.Before going into dynamical dark energy models, it is necessary to introduce the background knowledge of cosmology. Since general relativity's view of spacetime and dynamical equations are needed in order to understand modern cosmology, we briefly introduce these topics in the appendix. For the background cosmology, we first introduce the Robertson-Walker metric, the most general metric that is adapted to the cosmological principle, and derive dynamical equations from Einstein's equations with this metric. We then explore evolutions of a perfect fluid with given equations of state. Thereafter, we introduce the basic knowledge of particle physics, including standard model and beyond, as particle physics is essential to understand modern cosmology. After that, we explore the thermal history of the universe, i.e., the standard hot big bang model, reviewing important events in radiation , matter and dark energy dominated epochs respectively. On account of its similarity to dark energy, we introduce the primordial inflation model in the end of this part, a key modification to the hot big bang model.We then survey dark energy models. Firstly, we explore the cosmological constant model and indicate two major problems within it, that is, the fine-tuning and coincidence problems. Because of these two problems and consideration from particle physics theories as well as the status quo of observational data, we introduce dynamical dark energy (DDE) models and survey the basic ideas of several important DDE models, including quintessence, phantom, quintom, k-essence and holographical dark energy.Thereafter, we stick to the quintessence DDE models. By the definitions of the fine-tuning and coincidence problems in this thesis, DDE itself avoids the fine-tuning problem, so this part mainly focuses on how the quintessence models can alleviate the coincidence problem. We first briefly introduce the knowledge of autonomous dynamical system that is needed for analyzing the dynamics of quintessence. After simplifying the quintessence dynamical system, we focus on two types of models: tracking solutions and scaling solutions. Then we investigate implication of models that couple quintessence to ordinary matter for the coincidence problem.Finally, we turn to the innovative part of this thesis. In this part, we take a new approach to reconstruct quintessence potentials. With this approach, we first easily obtain a tracking solution that is different from those discovered previously, and straightforwardly find a solution of multiple attractors, i.e., a solution with more than one attractor for a given set of parameters. Then we propose a scenario of quintessence where the field jumps out of the scaling attractor to the de-Sitter-like attractor, by introducing a field whose value changes a certain amount in a short time, leading to the current acceleration. We also calculate the change the field needs for a successful jump and suggest a possible mechanism that involves spontaneous symmetry breaking to realize the sudden change of the field value.