Determining cosmological parameters from X-ray measurements of strong lensing clusters

We discuss a new method which is potentially capable of constraining cosmological parameters using observations of giant luminous arcs in rich X-ray clusters of galaxies. The mass profile and the mass normalization of the lenses are determined from X-ray measurements. The method also allows to probe the amount and equation of state of the dark energy in the universe. The analysis of a preliminary sample of 6 luminous, relatively relaxed clusters of galaxies strongly favours an accelerating expansion of the universe. Under the assumption that the dark energy is in the form of a cosmological constant, the data provide an estimate of $\Omega_\Lambda = 1.1$ with a statistical error of $\pm 0.2$. Including the constraint of a flat universe and an equation of state for the dark energy $w_X \geq -1$, we obtain $\Omega_M = 0.10 \pm 0.10$ and $w_X = -0.84 \pm 0.14$. Relaxing the prior on $w_X$, we find that the null energy condition is satisfied at the 3-$\sigma$ confidence level.