  Many multiply--imaged quasars have been found over the years, but none so far
with image separation in excess of $8\arcsec$. The absence of such large
splittings has been used as a test of cosmological models: the standard Cold
Dark Matter model has been excluded on the basis that it predicts far too many
large--separation double images. These studies assume that the lensing
structure has the mass profile of a singular isothermal sphere. However, such
large splittings would be produced by very massive systems such as clusters of
galaxies, for which other gravitational lensing data suggest less singular mass
profiles. Here we analyze two cases of mass profiles for lenses: an isothermal
sphere with a finite core radius (density $\rho \propto
(r^2+r_{core}^2)^{-1})$, and a Hernquist profile ($\rho \propto
r^{-1}(r+a)^{-3}$). We find that small core radii $r_{core} \sim 30 h^{-1}$
kpc, as suggested by the cluster data, or large $a \gsim 300 h^{-1}$ kpc, as
needed for compatibility with gravitational distortion data, would reduce the
number of large--angle splittings by an order of magnitude or more. Thus, it
appears that these tests are sensitive both to the cosmological model (number
density of lenses) and to the inner lens structure, which is unlikely to depend
sensitively on the cosmology, making it difficult to test the cosmological
models by large--separation quasar lensing until we reliably know the structure
of the lenses themselves.
