  The evolution of the quintessence in various stages of the universe, the
radiation-, matter-, and quintessence-dominated, is closely related with the
tracking behavior and the deceleration parameter of the universe. We gave the
explicit relation between the equation-of-state of the quintessence in the
epoch of the matter-quintessence equality and the inverse power index of the
quintessence potential, obtained the constraint on this potential parameter
come from the present deceleration parameter, i.e., a low inverse power index.
We point out that the low inverse power-law potential with a single term can
not work for the tracking solution. In order to have both of the tracker and
the suitable deceleration parameter it is necessary to introduce at least two
terms in the quintessence potential. We give the future evolution of the
quintessential universe.

Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology