Constraining the dark energy with galaxy clusters X-ray data

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 $p_x=\omega {\rho }_x$ we place the following limits on the cosmological parameters $\omega$ and ${\mathrm{\Omega }}_{\mathrm{m}}$: (i) $-1 \leq \omega \leq -0.55$and$\Omega_{\rm m} = 0.32^{+0.027}{-0.014}$(1$\sigma$) if the equation of state of the dark energy is restricted to the interval $-1 \leq \omega < 0$(\mathit{\text{usual}}quintessence)and(ii)$\omega = -1.29^{+0.686}{-0.792}$and$\Omega_{\rm{m}} = 0.31^{+0.037}_{-0.034}$($1\sigma$)if$\omega$violatesthenullenergyconditionandassumevalues$< -1$ (\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.