Based on the agreement between the z 3 and z 4 luminosity functions at the bright end, it has been recently argued  that the decline in the luminosity density of faint HDF Lyman-break galaxies observed in the same redshift interval  may not be real, but simply due to sample variance in the HDF. When extinction corrections are applied, the emissivity per unit comoving volume due to star formation may then remain essentially flat for all redshift z 1 (see Fig. 4). While this has obvious implications for hierarchical models of structure formation, the epoch of first light, and the reionization of the intergalactic medium (IGM), it is also interesting to speculate on the possibility of a constant star-formation density at all epochs 0 z 5. Figure 5 shows the time evolution of the blue and near-IR rest-frame luminosity density of a stellar population characterized by a Salpeter IMF, solar metallicity, and a (constant) star formation rate of * = 0.054 M yr-1 Mpc-3 (needed to produce the observed EBL). The predicted evolution appears to be a poor match to the observations: it overpredicts the local B and K-band luminosity densities, and underpredicts the 1 µm emissivity at z 1.
Figure 5. Left: Synthetic evolution of the near-IR luminosity density at rest-frame wavelengths of 1.0 (long-dashed line) and 2.2 µm (short-dashed line). The model assumes a constant star formation rate of * = 0.054 M (Salpeter IMF). The dotted (2.2 µm) and dash-dotted (1.0 µm) curves show the emissivity of a simple stellar population with formation redshift zon = 5, and total mass equal to the mass observed in spheroids today . The data points are taken from  (filled dots) and  (filled triangle). Right: Same but in the B-band. The data points are taken from  (filled dots),  (empty triangles), and  (empty squares).
At the other extreme, we know from stellar population studies that about half of the present-day stars are contained in spheroidal systems, i.e. elliptical galaxies and spiral galaxy bulges, and that these stars formed early and rapidly. The expected rest-frame blue and near-IR emissivity of a simple stellar population with formation redshift zon = 5 and total mass density equal to the mass in spheroids observed today is shown in Figure 5. In this model the near-IR and blue emissivities at z = 4-5 are comparable with the values observed at z = 1. HST-NICMOS deep observations may be able to test similar scenarios for the formation of elliptical galaxies at early times.