We examine the faint-end slope of the rest-frame V-band luminosity function (LF), with respect to galaxy spectral type, of field galaxies with redshift z<0.5, using a sample of 80,820 galaxies with photometric redshifts in the Cosmic Evolution Survey (COSMOS) field. For all galaxy spectral types combined, the LF slope, alpha, ranges from -1.24 to -1.12, from the lowest redshift bin to the highest. In the lowest redshift bin (0.02<z<0.1), where the magnitude limit is M(V) ~ -13, the slope ranges from ~ -1.1 for galaxies with early-type spectral energy distributions (SEDs), to ~ -1.9 for galaxies with low-extinction starburst SEDs. In each galaxy SED category (Ell, Sbc, Scd/Irr, and starburst), the faint-end slopes grow shallower with increasing redshift; in the highest redshift bin (0.4<z<0.5), the slope is ~ -0.5 and ~ -1.3 for early-types and starbursts respectively. The steepness of alpha at lower redshift could be qualitatively explained by large numbers of faint dwarf galaxies, perhaps of low surface brightness, which are not detected at higher redshifts.
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