  We use numerical simulations of galaxy clusters in different cosmologies to
study their ability to form large arcs. The cosmological models are: Standard
CDM (SCDM; Omega_0=1, Omega_Lambda=0); tauCDM with reduced small-scale power
(parameters as SCDM, but with a smaller shape parameter of the power spectrum);
open CDM (OCDM; Omega_0=0.3, Omega_Lambda=0); and spatially flat, low-density
CDM (LambdaCDM; Omega_0=0.3, Omega_Lambda=0.7). All models are normalised to
the local number density of rich clusters. Simulating gravitational lensing by
these clusters, we compute optical depths for the formation of large arcs. For
large arcs with length-to-width ratio >= 10, the optical depth is largest for
OCDM. Relative to OCDM, the optical depth is lower by about an order of
magnitude for LambdaCDM, and by about two orders of magnitude for S/tauCDM.
These differences originate from the different epochs of cluster formation
across the cosmological models, and from the non-linearity of the strong
lensing effect. We conclude that only the OCDM model can reproduce the observed
arc abundance well, while the other models fail to do so by orders of
magnitude.
