  A generic feature of cosmic quintessence models 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, for example as might be generated at the end of
"quintessential inflation." As such, these models can be constrained by
primordial nucleosynthesis and the epoch of photon decoupling. Here, we analyze
both kinetic dominated and power-law quintessence fields (with and without a
supergravity correction). We quantify the allowed initial conditions and
effective-potential parameters. We also deduce constraints on the epoch of
matter creation at the end of quintessential inflation.
