  Several independent lines of reasoning suggest that many of the very faint (B
> 24) blue galaxies are low-mass objects that experienced a short epoch of star
formation at redshifts 0.5 < z < 1 and have since faded into low luminosity,
low surface brightness objects. Such a scenario, which arises naturally if star
formation in dwarf galaxies is delayed by photoionisation due to the
metagalactic UV radiation field, provides an attractive way to reconcile the
Einstein-de Sitter cosmological model to the steeply rising galaxy counts
observed at blue wavelengths. The Hubble Deep Field (HDF) images provide a
stringent test of this model. We compare the Babul & Ferguson (1996) model to
the data by constructing using simulated images and carrying out source
detection and photometry for the simulations in the same way they were carried
out for the real data. We compare the model predictions for the counts, sizes,
and colours of galaxies observed in the HDF, and to the predictions from a low
q_0 pure-luminosity-evolution (PLE) model. Both models fail to reproduce the
observations. The low q_0 model predicts far more Lyman-break ``dropouts'' than
are seen in the data. The fading dwarf model predicts too many remnants: faded
dwarf galaxies in the redshift range 0.2 < z < 0.5 that should be detectable in
the HDF as low-surface brightness red objects but are not seen. If fading dwarf
galaxies are to reconcile the Einstein-de Sitter geometry to the counts, then
the dwarf population must (a) form earlier than z ~ 1, with a higher initial
luminosity; (b) have an initial-mass function more heavily weighted toward
massive stars than the Salpeter IMF; or (c) expand much more than assumed
during the supernova wind phase.
