On the inconsistency between cosmic stellar mass density and star
  formation rate up to $z\sim8$
  In this paper, we test the discrepancy between the stellar mass density and
instantaneous star formation rate in redshift range $0<z<8$ using a large
observational data sample. We first compile the measurements of the stellar
mass densities up to $z\sim 8$. Comparing the observed stellar mass densities
with the time-integral of instantaneous star formation history, we find that
the observed stellar mass densities are lower than that implied from star
formation history at $z<4$. We also use Markov chain monte carlo method to
derive the best-fitting star formation history from the observed stellar mass
density data. At $0.5<z<6$, the observed star formation rate densities are
larger than the best-fitting one, especially at $z\sim2$ where by a factor of
about two. However, at lower ($z<0.5$) and higher redshifts ($z>6$), the
derived star formation history is consistent with the observations. This is the
first time to test the discrepancy between the observed stellar mass density
and instantaneous star formation rate up to very high redshift $z\approx8$
using the Markov chain monte carlo method and a varying recycling factor.
Several possible reasons for this discrepancy are discussed, such as
underestimation of stellar mass density, initial mass function and cosmic
metallicity evolution.
