We use high-resolution N -body simulations to investigate the optical depth of giant arcs with length-to-width ratio larger than 7.5 and 10 in the ‘ standard ’ \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 \sim 6 compared with that in the ‘ standard ’ \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 , \sim 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 conventional assumptions of the background source population are correct .