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 CI 00 24+1654. The radial variation of their number density in the magnitude bins B = 26 - 28 and I = 24 - 26.5 displays an (anti)bias magnificati on effect similar to the one observed in A1689 by Broadhurst (1995) fo r I < 24. The study of this effect provides a determination of the rad ial distribution of critical lines of the gravitational lens from whic h 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 cr itical line near the large triple are. The depletion extends from R-B = 30 '' to R-B = 53 '' and the shape of the curve can almost be reprod uced with two redshift populations selected by the two filters. With o ur 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 redsh ift close to z = 3. The I selected population observed with the lens h as a broader depletion with a minimum extending from the B inner criti cal line to R-I = 60 ''. Whatever the cosmological model, the very fai nt I-selected galaxies spread up to a larger redshift with about 20% a bove z > 4. The fact that many faint I selected galaxies are not detec ted 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 gravi tational potential derived from a study of the large triple are seen a round the cluster, the locations of the two extreme critical lines for the B and I selected galaxies seems to favour Omega(Lambda)-dominated flat universes with a cosmological constant ranging from 0.6 to 0.9. The result is confirmed by a preliminary investigation of the Broadhur st's effect in A 370. However, ultra-deep detection of faint distant g alaxies down to the noise level are technically very difficult. In thi s first paper we mainly discuss the method to search the so-called ''l ast critical line'' and several possible effects which may bias the re sults on cosmological parameters. We conclude that the systematic meas urement of this outer critical line of the faint I selected galaxies p opulation around many clusters with gravitational arcs of known (low) redshift may help to count the number of faint galaxies at very large redshifts beyond the possibility of any spectroscopic survey, and even tually to settle the issue of the existence of the cosmological consta nt.