On Investigation Of The Accelerating Expansion Universe

The discovery of accelerating expansion of the universe imposes a great new challenge to the modern theory of physics and entrust a new mission to the scientific computation. Nowadays, human beings have entered into an era of precise cosmology: using the latest astronomical observations data, by the numerical method, calculate precise results and compare various theories, then give the best one. The current work explores some problems relevant to accelerating expansion of the universe by the numerical computation method and analytic method. We study two kinds of accelerating expansion theory which are viscous Cardassian universe and scalar torsion cosmology, respectively.The entire dissertation is divided into five chapters. We begin by giving some basic facts about our universe and the fundamental theory of cosmology based on the general relativity in Chapter 1. Besides, we review the classification of various accelerating cosmology models briefly. In Chapter 2, we discuss the dynamics and virialization of the viscous Cardassian models. The dynamical analysis indicates that there exists a singular curve in the phase space of viscous Cardassian model. In the viscous PL model, the equation-of-state parameter w_eff is no longer a constant and it can cross the cosmological constant divide w_∧= - 1, in contrast with same problem of the ordinary PL model. For MP and Exp models, w_eff evolves more near -1 than the case without viscosity. The virialization results show that the bulk viscosity retards the progress of collapse system. In Chapter 3 the torsion cosmology is studied. The dynamical attractor and heteroclinic orbit have been employed to make the late-time behaviors of the model insensitive to the initial condition and thus alleviate the fine-tuning problem in the torsion cosmology. We find that there are some typical characteristic of the evolution of statefinder parameters for the torsion cosmology that can be distinguished from the other cosmological models. The statefinder diagnostic divides the torsion parameter a₁ into differential ranges, which is in keeping with the requirement of dynamical analysis. Further discussion implies that the statefinder diagnostic has the advantage over the dynamical analysis at the simplicity, but the latter can provide more information. In Chapter 4, we fit the viscous Cardassian models and scalar torsion model to supernovae data and give the best fit values of the parameters. In the end, we give a conclusion and prospect.