The giant arc statistics in the three-year Wilkinson Microwave Anisotropy Probe cosmological model

We use high-resolution N-body simulations to investigate the optical depth of giant arcs with length-to-width ratios larger than 7.5 and 10 in the 'standard' Lambda cold dark matter (Lambda CDM) model with sigma(8) = 0.9 and Omega(m,0) = 0.3 and a model based on three-year Wilkinson Microwave Anisotropy Probe (WMAP) data. We find that, in dark-matter-only simulations, the lensing probability in the three-year WMAP model (with sigma(8) = 0.74 and Omega(m,0) = 0.238) decreases by a factor of similar to 6 compared with that in the 'standard' Lambda cold dark matter (Lambda CDM) model. The effects of baryonic cooling, star formation and feedbacks are uncertain, but we argue that baryons will only increase the the lensing cross-section by a moderate factor, similar to 2. We conclude that the low central value of sigma(8) and Omega(m,0) preferred by the WMAP three-year data may be too low to be compatible with observations if the conventional assumptions of the background source population are correct.