Distribution of galaxies at large redshift and cosmological parameters from the magnification bias in Cl 0024 + 1654 ?

We analyse the surface density of very faint galaxies at the limit of the sky background noise in the field of the cluster of galaxies Cl 0024+1654. The radial variation of their number density in the magnitude bins B = 26 − 28 and I = 24 − 26.5 displays an (anti)bias magnification effect similar to the one observed in A1689 by Broadhurst (1995) for I < 24. The study of this effect provides a determination of the radial distribution of critical lines of the gravitational lens from which we infer the redshift range of the populations seen in B and I. The surface density of B galaxies drops rapidly to a well-defined inner critical line near the large triple arc. The depletion extends from R B = 30 " to R B = 53 " and the shape of the curve can almost be reproduced with two redshift populations selected by the two filters. With our data 60% ± 10% of the B-selected galaxies are between z = 0.9 and z = 1.1 while most of the remaining 40% galaxies should be at a redshift close to z = 3. The I selected population observed with the lens has a broader depletion with a minimum extending from the B inner critical line to R I = 60 ". Whatever the cosmological model, the very faint I-selected galaxies spread up to a larger redshift with about 20% above z > 4. The fact that many faint I selected galaxies are not detected in B also favour the existence of a more distant population with a redshift range between z = 3 and z = 4.5. Using a model for the gravitational potential derived from a study of the large triple arc seen around the cluster, the locations of the two extreme critical lines for the B and I selected galaxies seems to favour Ω Λ-dominated flat universes with a cosmologi-cal constant ranging from 0.6 to 0.9. The result is confirmed by a preliminary investigation of the Broadhurst's effect in A 370. However, ultra-deep detection of faint distant galaxies down to the noise level are technically very difficult. In this first paper we mainly discuss the method to search the so-called " last critical line " and several possible effects which may bias the results on cosmological parameters. We conclude that the systematic measurement of this outer critical line of the …