For over a decade , it has been debated whether the concordance \Lambda CDM model is consistent with the observed abundance of giant arcs in clusters .
While previous theoretical studies have focused on properties of the lens and source populations , as well as cosmological effects such as dark energy , the impact of initial conditions on the giant-arc abundance is relatively unexplored .
Here , we quantify the impact of non-Gaussian initial conditions with the local bispectrum shape on the predicted frequency of giant arcs .
Using a path-integral formulation of the excursion set formalism , we extend a semi-analytic model for calculating halo concentrations to the case of primordial non-Gaussianity , which may be useful for applications outside of this work .
We find that massive halos tend to collapse earlier in models with positive f _ { \mathrm { NL } } , relative to the Gaussian case , leading to enhanced concentration parameters .
The converse is true for f _ { \mathrm { NL } } < 0 .
In addition to these effects , which change the lensing cross sections , non-Gaussianity also modifies the abundance of supercritical clusters available for lensing .
These combined effects work together to either enhance ( f _ { \mathrm { NL } } > 0 ) or suppress ( f _ { \mathrm { NL } } < 0 ) the probability of giant-arc formation .
Using the best value and 95 \% confidence levels currently available from the Wilkinson Microwave Anisotropy Probe , we find that the giant-arc optical depth for sources at z _ { s } \sim 2 is enhanced by \sim 20 \% and \sim 45 \% for f _ { \mathrm { NL } } = 32 and 74 respectively .
In contrast , we calculate a suppression of \sim 5 \% for f _ { \mathrm { NL } } = -10 .
These differences translate to similar relative changes in the predicted all-sky number of giant arcs .