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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, $Ω_φ$, 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 $Ω_φ$ at temperatures near $T ∼ 1MeV$. We point out that current experimental data does not support the presence of such a field, providing the strong constraint $Ω_φ(MeV) < 0.045$ at $2σ$ 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 $Ω_φ ≤ 0.39$ at $2σ$ during the radiation dominated epoch.
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