As an alternative to solving the computationally demanding lens equations, Cen et al. [20] developed a more efficient scheme to identify regions with surface densities capable of generating multiple images accurately for splittings larger than three arcseconds. They applied this technique to a standard CDM model with , and found that this model predicts more large angle splittings (> 8'') than are known to exist in the observed Universe. Their results suggest that the standard CDM model should be excluded as a viable model of our Universe. A similar analysis for a flat low density CDM model with a cosmological constant (, ) suggests a lower and perhaps acceptable number of lensing events. However, an uncertainty in their studies is the nature of the lenses at and below the resolution of the numerical grid. They model the lensing structures as simplified Singular Isothermal Spheres (SIS) with no distinctive cores.

Large angle splittings are generally attributed to larger
structures such as clusters of galaxies, and there are
indications that clusters have small but finite core radii
kpc, where
*h*
is the Hubble parameter. Core radii of this size can have an
important effect on the probability of multiple imaging. Flores
and Primack [31] considered the effects of assuming two different kinds of
splitting sources: isothermal spheres with small but finite core
radii
, and spheres with a Hernquist density profile
, where
kpc and
kpc. They find that the computed frequency of large-angle
splittings, when using the nonsingular profiles, can potentially
decrease by more than an order of magnitude relative to the SIS
case and can bring the standard CDM model into better agreement
with observations. They stress that lensing events are sensitive
to both the cosmological model (essentially the number density of
lenses) and to the inner lens structure, making it difficult to
probe the models until the structure of the lenses, both
observationally and numerically, is better known.

Physical and Relativistic Numerical Cosmology
Peter Anninos
http://www.livingreviews.org/lrr-1998-2
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