  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.
