Constraining the dark energy with galaxy cluster 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 ${\Omega }_{\mathrm{m}}:$ (i) $-1<~\omega <~-0.55$ and ${\Omega }_{\mathrm{m}}{=0.32\mathrm{}}_{-0.014}^{+0.027\mathrm{}}$ $\left(1\mathrm{}\sigma \right)$ if the equation of state of the dark energy is restricted to the interval $-1<~\omega <0\mathrm{}$ (the usual quintessence) and (ii) $\omega =-{1.29}_{-0.792}^{+0.686\mathrm{}}$ and ${\Omega }_{\mathrm{m}}{=0.31\mathrm{}}_{-0.034}^{+0.037\mathrm{}}$ $\left(1\mathrm{}\sigma \right)$ if $\omega$ violates the null energy condition and assume values below $-1$ (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.