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.

11 pages, 3 figures, PRD vol 65 (002) in press