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 ${\mathrm{\Omega }}_{\mathrm{\Lambda }}=1.1$ with a statistical error of $\pm 0.2$. Including the constraint of a flat universe and an equation of state for the dark energy $w_X\ge -1$, we obtain ${\mathrm{\Omega }}_M=0.10\pm 0.10$ 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.