Unavoidable Selection Effects in the Analysis of Faint Galaxies in the   Hubble Deep Field: Probing the Cosmology and Merger History of Galaxies
  (Abridged) We present a detailed analysis of the number count and photometric redshift distribution of faint galaxies in the Hubble Deep Field (HDF), paying a special attention to the selection effects including the cosmological dimming of surface brightness of galaxies. We find a considerably different result from previous studies ignoring the selection effects, and 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 > 3-4 must be invoked to reproduce the I_{814} counts, when parametrized as \phi^* \propto (1+z)^\eta. However we show that such a strong number evolution under realistic merging processes of galaxies can not 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 > 0.2, but 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 ~ 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. 
Tomonori Totani (NAO, Japan) and Yuzuru Yoshii (IoA, U. Tokyo)