Cosmology through arc statistics I: sensitivity to Ωm and σ8

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 normalization of the primordial power spectrum, expressed in terms of as. 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 <= Omega(m) < 0.5 and 0.6 <= sigma(8) <= 1. We find that the arc counts dependence on Omega(m) and as 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 depend on the survey area. We find that the constraining power of arc statistics degrades critically only for surveys covering an area smaller than 10 per cent 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 per cent of the arcs will be missed, with only a small degradation of the corresponding cosmological constraints.