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.Comment: 24 pages including 5 figures, accepted to ApJ