Constraining the quintessence equation of state with SnIa data and CMB peaks

Quintessence has been introduced as an alternative to the cosmological constant scenario to account for the current acceleration of the universe. This new dark energy component allows values of the equation of state parameter $w_Q^0>~-1$ and in principle measurements of cosmological distances to type Ia supernovae can be used to distinguish between these two types of models. Assuming a flat universe, we use the supernovae data and measurements of the position of the acoustic peaks in the cosmic microwave background spectra to constrain a rather general class of quintessence potentials, including inverse power law models and recently proposed supergravity inspired potentials. In particular we use a likelihood analysis, marginalizing over the dark energy density ${\Omega }_Q,$ the physical baryon density ${\Omega }_b{h}^2$ and the scalar spectral index n, to constrain the slopes of our quintessence potential. Considering only the first Doppler peak the best fit in our range of models gives $w_Q^0\sim -\mathrm{0.8.}$ However, including the SnIa data and the three peaks, we find an upper limit on the present value of the equation of state parameter, $-1<~w_Q^0<~-0.93$ at $2\sigma ,$ a result that appears to rule out a class of recently proposed potentials.