Friedmann, Equation, And The Accelerating Expansion Of The Universe

In this master dissertation, we study the relation between the modification to the Friedmann equation and the accelerated expansion of our universe. Using phase space methods, the dynamics of the universe are analyzed. Additionally, we study the virialization of two Cardassian models proposed by us. The paper is arranged as following.Firstly, we briefly review the moden cosmology and the classification of the dark energy.Secondly, we propose a phantom model with double exponential potential and analyze it's dynamics. The complete classification of solutions are given according to their late-time behavior. Especially, a heteroclinic solution which is an orbit connecting two different critical points in contrast with the case of quintessence.Thirdly, we give a brief introduction of the Cardassian universe and then analyze the dynamics of two Cardassian models .Finally, the exponential Cardassian universe are proposed. In the following, it's dynamics and virialization are studied. We also fit the model parameters to current supernova data. Furthermore, we point out that the equation-of-state parameter for the effective dark fluid component in exponential Cardassian models can naturally cross the cosmological constant divide w = -1 that observations favor mildly without introducing exotic material that destroy the weak energy condition. We also found that the Cardassian term held back the process of galaxies formation, and the ratioR_vir / R_ta in the case where the whole system virializes increase faster than that underthe circumstances where only matter virializes.