  The acceleration of the cosmic expansion revealed by supernova observations
indicates that the present universe is dominated by repulsive dark energy. It
is natural that the coupling between the dark energy and the attractive gravity
has to be taken into account in studying the evolution of our universe. Here we
induce a dynamic equation of universe evolution based on the cosmological
principal, gravity-dark energy coupling, and energy conservation. The solutions
of this dynamic equation provide a specific picture of cosmic evolution, which
is well compatible with current observed evolution histories of both Hubble
parameter H(z) and equation of state parameter w(z) of dark energy. In this
picture, the already observed universe has undergone through three epochs - the
epoch of equilibrium between gravity and dark energy at cosmological redshifts
z>1, the phase transition epoch at z between about 0.5 and 1, and the present
acceleration epoch starting from z~0.5. The expected matter-dominated
deceleration epoch has not been seen yet, which requires future deep
observations to look back upon more early universe.
