The effects of primordial non-Gaussianity on giant-arc statistics

Abstract

For over a decade, it has been debated whether the concordance Λ cold dark matter (ΛCDM) 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 haloes tend to collapse earlier in models with positive fNL, relative to the Gaussian case, leading to enhanced concentration parameters. The converse is true for fNL < 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 (fNL > 0) or suppress (fNL < 0) the probability of giant-arc formation. Using the best value and 95 per cent confidence levels currently available from the Wilkinson Microwave Anisotropy Probe, we find that the giant-arc optical depth for sources at zs∼ 2 is enhanced by ∼20 and ∼45 per cent for fNL= 32 and 74, respectively. In contrast, we calculate a suppression of ∼5 per cent for fNL=−10. These differences translate to similar relative changes in the predicted all-sky number of giant arcs.