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 spec ial attention to selection effects, including the cosmological dimming of t he surface brightness of galaxies, under the observational conditions emplo yed in this field. We find a considerably different result from previous st udies that ignore selection effects; these effects should therefore be take n into account in the analysis. We find that the model of pure luminosity e volution (PLE) of galaxies in the Einstein-de Sitter (EdS) universe predict s much smaller counts than those observed at faint magnitude limits, by a f actor of more than 10, so that a very strong number evolution of galaxies w ith eta greater than or similar to 3-4 must be invoked to reproduce the I-8 14 counts, when parametrized as phi* proportional to (1 + z)(pi). However, we show that such a strong number evolution under realistic merging process es of galaxies cannot explain the steep slope of the B-450 and V-606 counts , and it is seriously inconsistent with their photometric redshift distribu tion. We find that these difficulties still persist in an open universe wit h Omega(0) greater than or similar to 0.2, and are resolved only when we in voke a Lambda-dominated flat universe, after examining various systematic u ncertainties in modeling the formation and evolution of galaxies. The prese nt analysis revitalizes the practice of using faint number counts as an imp ortant cosmological test, giving one of the arguments against the EdS unive rse, and suggests acceleration of the cosmic expansion by vacuum energy den sity. 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 stro nger number evolution with eta > 1 is rejected from the HDF data, giving a strong constraint on the merger history of galaxies.