The equation of state characterizing the dark energy component is constrained
by combining Chandra observations of the X-ray luminosity of galaxy clusters
with independent measurements of the baryonic matter density and the latest
measurements of the Hubble parameter as given by the HST key project. By
assuming a spatially flat scenario driven by a "quintessence" component with an
equation of state px=ωρx we place the following limits on the
cosmological parameters ω and Ωm: (i) −1≤ω≤−0.55 and Ωm=0.32−0.014+0.027 (1σ) if the
equation of state of the dark energy is restricted to the interval −1≤ω<0 (\emph{usual} quintessence) and (ii) ω=−1.29−0.792+0.686 and Ωm=0.31−0.034+0.037
(1σ) if ω violates the null energy condition and assume values <−1 (\emph{extended} quintessence or ``phantom'' energy). These results are in
good agreement with independent studies based on supernovae observations,
large-scale structure and the anisotropies of the cosmic background radiation.Comment: 6 pages, 4 figures, LaTe