Vacuum energy reduction through destabilization: a unification of quintessence and a dynamical approach?

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.