Cosmological parameter estimation in the quintessence paradigm

We present cosmological parameter constraints on flat cosmologies dominated by dark energy using various cosmological data including the recent Archeops angular power spectrum measurements. A likelihood analysis of the existing Cosmic Microwave Background data shows that in the absence of further prior, dark energy is not required. This comes from the fact that degeneracies exist among the various cosmological parameters constrained by the Cosmic Microwave Background. We found that there is a degeneracy in a combination of the Hubble parameter H0 and of the dark energy equation of state parameter W Q, but that W Q is not correlated with the primordial index n of scalar fluctuations and the baryon content .... The preferred primordial index is n=0.95+-0.05(68%)and baryon content .... Adding constraints on the amplitude of matter fluctuations on small scales, (sigma) 8, obtained from clusters abundance or weak lensing data may allow degenaracies to be broken, although present-day systematic uncertainties do not allow for firm conclusions as yet. Further addition of the Hubble Space Telescope measurements of the local distance scale and of the high redshift supernovae data allow one to obtain tight constraints. When these constraints are combined we find that the amount of dark energy is 0.7^+0.10-0.07 ( 95%C.L.) and that its equation of state is very close to those of the vacuum: W Q<-0.75(> 95% C.L.). In no case do we find that quintessence is prefered over the classical cosmological constant, although robust data on (sigma)8 might rapidly shed light on this important issue.