Unavoidable selection effects in the analysis of faint galaxies in the Hubble Deep Field: Probing the cosmology and merger history of galaxies

We present a detailed analysis of the number count and photometric redshift distribution of faint galaxies in the Hubble Deep Field (HDF), paying special attention to selection effects, including the cosmological dimming of the surface brightness of galaxies, under the observational conditions employed in this field. We find a considerably different result from previous studies that ignore selection effects; these effects should therefore be taken into account in the analysis. We find that the model of pure luminosity evolution (PLE) of galaxies in the Einstein-de Sitter (EdS) universe predicts much smaller counts than those observed at faint magnitude limits, by a factor of more than 10, so that a very strong number evolution of galaxies with eta greater than or similar to 3-4 must be invoked to reproduce the I(814) counts, when parametrized as phi* proportional to (1 + z)(pi). However, we show that such a strong number evolution under realistic merging processes of galaxies cannot explain the steep slope of the B(450) and V(606) counts, and it is seriously inconsistent with their photometric redshift distribution. We find that these difficulties still persist in an open universe with Omega(0) greater than or similar to 0.2, and are resolved only when we invoke a Lambda-dominated flat universe, after examining various systematic uncertainties in modeling the formation and evolution of galaxies. The present analysis revitalizes the practice of using faint number counts as an important cosmological test, giving one of the arguments against the EdS universe, and suggests acceleration of the cosmic expansion by vacuum energy density. While a modest number evolution of galaxies with eta greater than or similar to 1 is still necessary even in a Lambda-dominated universe, a stronger number evolution with eta > 1 is rejected from the HDF data, giving a strong constraint on the merger history of galaxies.