  The cosmic gamma-ray burst (GRB) formation rate, as derived from the
variability-luminosity relation for long-duration GRBs, is compared with the
cosmic star formation rate. If GRBs are related to the collapse of massive
stars, one expects the GRB rate to be approximately proportional to the star
formation rate. We found that these two rates have similar slopes at low
redshift. This suggests that GRBs do indeed track the star formation rate of
the Universe, which in turn implies that the formation rate of massive stars
that produce GRBs is proportional to the total star formation rate. It also
implies that we might be able to use GRBs as a probe of the cosmic star
formation rate at high redshift. We find that the cosmic star formation rate
inferred from the variability-luminosity relation increases steeply with
redshift at z > 3. This is in apparent contrast to what is derived from
measurements of the cosmic star formation rate at high redshift from optical
observations of field galaxies, suggesting that much high-z star formation is
being missed in the optical surveys, even after corrections for dust extinction
have been made.
