On Arcs and Omega

The gravitational lens effect of galaxy clusters can produce large arcs from source galaxies in their background. Typical source redshifts of ~ 1 require clusters at z ~ 0.3 for arcs to form efficiently. Given the cluster abundance at the present epoch, the fewer clusters exist at z ~ 0.3 the higher Omega_0 is, because the formation epoch of galaxy clusters strongly depends on Omega_0. In addition, at fixed Omega_0, clusters are less concentrated, and hence less efficient lenses, when the cosmological constant is positive, Omega_Lambda > 0. Numerical cluster simulations show that the expected number of arcs on the sky is indeed a sensitive function of Omega_0 and Omega_Lambda. The numerical results are compatible with the statistics of observed arcs only in a universe with low matter density, Omega_0 ~ 0.3, and zero cosmological constant. Other models fail by one or two orders of magnitude, rendering arc statistics a sensitive probe for cosmological parameters.