Distribution of galaxies at large redshift and cosmological parameters from the magnification bias in Cl0024+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 Cl0024+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 for $I<24$ which provides the redshift range of the populations seen in $B$ and $I$. The depletion curve can be reproduced with two redshift populations with $60% \pm 10%$ofthe$B$galaxiesbetween$z=0.9$and$z=1.1$ and the remaining at a redshift close to $z=3$. The $I$ selected population is similar but with a minimum extending from the $B$ inner critical line to $R_I=60\mathrm{"}$. Whatever the cosmological model, the $I$-selected galaxies spread up to a larger redshift with about 20% above $z>4$. Using a model for the gravitational potential, the locations of the two extreme critical lines for the B and I galaxies favour ${\mathrm{\Omega }}_{\mathrm{\Lambda }}$-dominated flat universes with a cosmological constant ranging from 0.6 to 0.9. The result is confirmed by a preliminary investigation of A370. We discuss the method to search the “last critical line” and the various biases.