Cosmology through arc statistics I: sensitivity to $\Omega_m$ and $\sigma_8$

TL;DR

This paper investigates how arc statistics from gravitational lensing can constrain cosmological parameters like m and , demonstrating their sensitivity and potential for future large sky surveys.

Contribution

It presents the first detailed analysis of arc count sensitivity to m and , including effects of survey area and cluster-based arc detection strategies.

Findings

Arc counts are sensitive to m and , with similar but not identical dependence as halo counts.

Survey areas smaller than 10% of the sky significantly reduce constraining power.

Cluster-based arc searches miss less than 10% of arcs, minimally impacting constraints.

Abstract

The next generation of large sky photometric surveys will finally be able to use arc statistics as a cosmological probe. Here we present the first of a series of papers on this topic. In particular, we study how arc counts are sensitive to the variation of two cosmological parameters: the (total) matter density parameter, $\Omega_m$, and the normalisation of the primordial power spectrum, expressed in terms of $\sigma_8$. Both these parameters influence the abundances of collapsed structures and their internal structure. We compute the expected number of gravitational arcs with various length-to-width ratios in mock light cones, by varying these cosmological parameters in the ranges $0.1\leq\Omega_m\leq0.5$ and $0.6\leq\sigma_8\leq 1$. We find that the arc counts dependence on $\Omega_m$ and $\sigma_8$ is similar, but not identical, to that of the halo counts. We investigate how the precision of the constraints on the cosmological parameters based on arc counts depends on the survey area. We find that the constraining power of arc statistics degrades critically only for surveys covering an area smaller than $10\%$ of the whole sky. Finally, we consider the case in which the search for arcs is done only in frames where galaxy clusters have been previously identified. Adopting the selection function for galaxy clusters expected to be detected from photometric data in future wide surveys, we find that less than $10\%$ of the arcs will be missed, with only a small degradation of the corresponding cosmological constraints.