QUINTESSENCE AND THE CURVATURE OF THE UNIVERSE AFTER WMAP

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Abstract
We study quintessence models with a constant (effective) equation of state. It is investigated whether such quintessence models are consistent with a negative spatial curvature of the Universe with respect to the anisotropy of the cosmic microwave background radiation measured by the WMAP mission. If the reionization is negligibly small, it is found that such models with negative curvature are admissible due to a geometrical degeneracy. However, a very high optical depth τ to the surface of last scattering, as indicated by the polarization measurements of WMAP, would rule out such models.