  Recently, attempts have been made to understand the apparent near coincidence
of the present dark energy and matter energy in terms of a dynamical
attractor-like solution for the evolution of a scalar field. In these models
the field couples with the dominant constituent and only acts like a
cosmological constant after the onset of the matter-diminated epoch. A generic
feature of such solutions, however, is the possibility of significant energy
density in the scalar field during the radiation-dominated epoch. This
possibility is even greater if the quintessence field begins in a
kinetic-dominated regime generated at the end of quintessential inflation. As
such, these models can affect and be constrained by primordial nucleosynthesis
and the epoch of of photon decoupling. Here, we analyze one popular form of the
quintessence field (with and without a supergravity correction) and quantify
constraints on the allowed initial conditions and parameters for the effective
potential. We also deduce constraints on the epoch of matter creation at the
end of quintessential inflation.
