  Although quintessence cosmologies seem to explain the amount of cosmological
constant today, the required conditions are severe. For example, an extremely
slowly varying and light scalar field that rolls toward the vanishing vacuum
energy state is needed, which must satisfy the required initial conditions so
that the energy density in matter is comparable to the energy density stored in
quintessence today. Our first question is whether it is possible to explain why
quintessence ``knows'' that the Universe is going toward the vanishing energy
state. We show from a new perspective that the conventional $O(H)$ corrections
may reproduce the required potential. Our second question is whether it is
possible to obtain plausible amount of the potential energy density today
without tuning initial conditions. Since our resultant potentials mimic
quintessence, one may solve the coincidence problem using the conventional
techniques for solving the coincidence problem in quintessence cosmology.
However, in our scenario we have another option, which is qualitatively
different from the one that have been discussed in quintessence cosmology.
Besides quintessence cosmology, we show that there is a relation between a
dynamical approach, which suggests that we can solve the coincidence problem in
a dynamical approach. As far as we know, this is the first attempt to discuss
about the unified picture and the important relations between these distinctive
scenarios.
