Constraints on the inner cluster mass profile and the power spectrum normalization from strong lensing statistics

Strong gravitational lensing is a useful probe of both the intrinsic properties of the lenses and the cosmological parameters of the universe. The large number of model parameters and small sample of observed lens systems, however, have made it difficult to obtain useful constraints on more than a few parameters from lensing statistics. Here we examine how the recent Wilkinson Microwave Anisotropy Probe measurements help improve the constraining power of statistics from the Cosmic Lens All-Sky Survey ( CLASS). We find that the absence of theta > 3" lenses in CLASS places an upper bound of beta < 1.25 (1.60) at a 68% (95%) confidence level (CL) on the inner density profile, rho proportional to r(-beta) of cluster-sized halos. Furthermore, the favored power spectrum normalization is sigma(g) greater than or similar to 0.7 (95% CL). We discuss two possibilities for stronger future constraints: a positive detection of at least one large-separation system and next-generation radio surveys such as the proposed Low-Frequency Array.