  The Einstein radius of a cluster provides a relatively model-independent
measure of the mass density of a cluster within a projected radius of ~ 150
kpc, large enough to be relatively unaffected by gas physics. We show that the
observed Einstein radii of four well-studied massive clusters, for which
reliable virial masses are measured, lie well beyond the predicted distribution
of Einstein radii in the standard LambdaCDM model. Based on large samples of
numerically simulated cluster-sized objects with virial masses ~ 1e15 solar,
the predicted Einstein radii are only 15-25'', a factor of two below the
observed Einstein radii of these four clusters. This is because the predicted
mass profile is too shallow to exceed the critical surface density for lensing
at a sizable projected radius. After carefully accounting for measurement
errors as well as the biases inherent in the selection of clusters and the
projection of mass measured by lensing, we find that the theoretical
predictions are excluded at a 4-sigma significance. Since most of the free
parameters of the LambdaCDM model now rest on firm empirical ground, this
discrepancy may point to an additional mechanism that promotes the collapse of
clusters at an earlier time thereby enhancing their central mass density.
