  Theoretical arguments and indirect observational evidence suggest that the
stellar initial mass function (IMF) may evolve with time, such that it is more
weighted toward high mass stars at higher redshift. Here we test this idea by
comparing the rate of luminosity evolution of massive early-type galaxies in
clusters at 0.02<z<0.83 to the rate of their color evolution. A combined fit to
the rest-frame U-V color evolution and the previously measured evolution of the
M/L_B ratio gives x~-0.3 for the logarithmic slope of the IMF in the region
around 1 Solar mass, flatter than the present-day value in the Milky Way disk
of x=1.3. The best-fitting luminosity-weighted formation redshift of the stars
in massive cluster galaxies is ~3.7, and a possible interpretation is that the
characteristic mass m_c had a value of ~2 Solar masses at z~4 (compared to
m_c~0.1 Solar masses today), in qualitative agreement with models in which the
characteristic mass is a function of the Jeans mass in molecular clouds. Such a
``bottom-light'' IMF for massive cluster galaxies has significant implications
for the interpretation of measurements of galaxy formation and evolution.
Applying a simple form of IMF evolution to literature data, we find that the
volume-averaged star formation rate at high redshift may have been
overestimated (by a factor of 3-4 at z>4), and the cosmic star formation
history may have a fairly well-defined peak at z~1.5. The M/L_V ratios of
galaxies are less affected than their star formation rates, and future data on
the stellar mass density at z>3 will provide further constraints on IMF
evolution. The formal errors likely underestimate the uncertainties, and
confirmation of thes results requires a larger sample of clusters and the
inclusion of redder rest-frame colors in the analysis.
