  Wide-separation lensed QSOs measure the mass function and evolution of
massive galaxy clusters, in a similar way to the cluster mass function deduced
from X-ray-selected samples or statistical measurements of the
Sunyaev-Zeldovich effect. We compute probabilities of strong lensing of QSOs by
galaxy clusters in dark energy cosmologies using semianalytical modelling and
explore the sensitivity of the method to various input parameters and
assumptions. We highlight the importance of considering both the variation of
halo properties with mass, redshift and cosmology and the effect of cosmic
scatter in halo concentration. We then investigate the extent to which
observational surveys for wide-separation lensed QSOs may be used to measure
cosmological parameters such as the fractional matter density Omega_M, the rms
linear density fluctuation in spheres of 8 Mpc/h, sigma_8, and the dark energy
equation of state parameter w. We find that wide-separation lensed QSOs can
measure sigma_8 and Omega_M in an equivalent manner to other methods such as
cluster abundance studies and cosmic shear measurements. In assessing whether
lensing statistics can distinguish between values of w, we conclude that at
present the uncertainty in the calibration of sigma_8 in quintessence models
dominates the conclusions reached. Nonetheless, lensing searches based on
current QSO surveys such as the Two-degree Field and the Sloan Digital Sky
Survey with 10^4-10^5 QSOs should detect systems with angular separations
greater than 5'' and hence can provide an important test of the standard
cosmological model that is complementary to measurements of cosmic microwave
background anisotropies.
