Multi-scalar Field Universe Dynamics

In this master dissertation, under the fundamental frame of general relativity, we study the dark energy and inflation in the early Universe.The thesis is consisted of five chapters. In Chapter 1, in order to make a theoretical preparation for the following discussion, we briefly review the basic theory of cosmology which includes the standard cosmology, the hot big bang cosmology and the cosmological inflation.In chapter 2, we report the recent cosmological observational results and the development of theory. The two logical possibilities for dark energy are the cosmological constant and quintessence, which has caught much attention ever since its invention and been mainly discussed.The properties of the attractor solutions of exponential potentials can lead to models of quintessence. And exponential potentials can arise from M theory. In chapter 3, we study the cosmological dynamics of barotropic fluid and scalar field with a double exponential potential and point out that the late-time asymptotic-behavior does not always corresponding to the single-exponential case. The dynamical attractor of the cosmological system has been employed to make the late time behaviors of the model insensitive to the initial condition of the field and thus alleviates the fine tuning problem. Combining the information from the critical points analysis with numerical solutions, we can reveal most of their properties.In chapter 4, firstly, we introduce the O(N) quintessence and make a new generalization to the discussion in chapter 3 for this model.In chapter 5, we wish to point out the possibility of using a complex scalar field to account for the inflationary stage and the current acceleration.A renormalizable complex scalar field Φ described by a lagrangian with a U(1) symmetry spontaneously broken at a high energy scale and explicitly broken by instanton effects at a much lower energy can account for both the early inflationary phase and the recent accelerated expansion of the Universe. We study a realistic model of quintessential inflation with radiation and matter. By the analysis of the dynamical system and numerical work about the evolution of the equation of state and cosmic density parameter, we show that this model is a good match for the current astronomical observation. Therefore, this model is more natural to explain the two stages of acceleration.