In the past years ’ quintessence ’ models have been considered which can produce the accelerated expansion in the universe suggested by recent astronomical observations .
One of the key differences between quintessence and a cosmological constant is that the energy density in quintessence , \Omega _ { \phi } , could be a significant fraction of the overall energy even in the early universe , while the cosmological constant will be dynamically relevant only at late times .
We use standard Big Bang Nucleosynthesis and the observed abundances of primordial nuclides to put constraints on \Omega _ { \phi } at temperatures near T \sim 1 MeV .
We point out that current experimental data does not support the presence of such a field , providing the strong constraint \Omega _ { \phi } ( \mbox { MeV } ) < 0.045 at 2 \sigma C.L .
and strengthening previous results .
We also consider the effect a scaling field has on CMB anisotropies using the recent data from Boomerang and DASI , providing the CMB constraint \Omega _ { \phi } \leq 0.39 at 2 \sigma during the radiation dominated epoch .