Recent progress in our understanding of faint galaxy data made possible by the combination of Hubble Space Telescope (HST) deep imaging and ground-based spectroscopy has vastly improved our understanding of the evolution of the stellar birthrate in optically-selected galaxies from the present-epoch up to z 4 (Steidel et al. 1998; Madau et al. 1998; Ellis 1997). The large increase in the quantity of information available on the high-redshift universe at optical wavelengths has been complemented by measurements of the far-IR/sub-mm background by DIRBE and FIRAS onboard the COBE satellite (Hauser et al. 1998; Fixsen et al. 1998; Schlegel et al. 1998; Puget et al. 1996), showing that a significant fraction of the energy released by stellar nucleosynthesis is re-emitted as thermal radiation by dust (Dwek et al. 1998), and by theoretical progress made in understanding how intergalactic gas follows the dynamics dictated by dark matter halos until radiative, hydrodynamic, and star formation processes take over (Kauffmann et al. 1993; Baugh et al. 1998; Somerville et al. 1999; Nagamine et al. 1999). Of perhaps equal importance for galaxy formation studies appear the recent findings of the microlensing experiments in the direction of the LMC, which suggest that between 20 and 100% of the dark matter in the Galactic halo is tied up in 0.5+0.3-0.2 M objects (Alcock et al. 1997). The underlying goal of all these efforts is to understand the growth of cosmic structures, the internal properties of galaxies and their evolution, and ultimately to map the star formation history of the universe from the end of the cosmic ``dark age'' to the present epoch.
In this paper we focus on the galaxy number-apparent magnitude relation and its first moment, the integrated galaxy contribution to the extragalactic background light (EBL). The logarithmic slope of the differential galaxy counts is a remarkably simple cosmological probe of the history of stellar birth in galaxies, as it must drop below 0.4 to yield a finite value for the EBL. Together with the far-IR/sub-mm background, the optical EBL from both resolved and unresolved extragalactic sources is an indicator of the total luminosity of the universe, as the cumulative emission from young and evolved galactic systems, as well as from active galactic nuclei (AGNs), is recorded in this background. As such it provides, for a given stellar mass function, a quantitative estimate of the baryonic mass that has been processed by stars throughout cosmic history.
Unless otherwise stated, an Einstein-de Sitter (EdS) cosmology (M = 1, = 0) with H0 = 100 h km s-1 Mpc-1 will be adopted in the following. All magnitudes will be given in the AB system.