Solutions of Friedmann's Equations and Cosmological Consequences

The Einstein equations of general relativity reduce, when the spacetime metric is of the Friedmann--Lemaitre--Robertson--Walker type governing an isotropic and homogeneous universe, to the Friedmann equations, which is a set of nonlinear ordinary differential equations, determining the law of evolution of the spatial scale factor, in terms of the Hubble ``constant''. It is a challenging task, not always possible, to solve these equations. In this talk, we present some insights from solving and analyzing the Friedmann equations and their implications to evolutionary cosmology. In particular, in the Chaplygin fluid universe, we derive a universal formula for the asymptotic exponential growth rate of the scale factor which indicates that, as far as there is a tiny presence of nonlinear (exotic) matter, linear (conventional) matter makes contribution to the dark energy, which becomes significant near the phantom divide line. Joint work with Shouxin Chen, Gary W. Gibbons, and Yijun Li.