The effect of the environment-dependent IMF on the formation and
  metallicities of stars over the cosmic history
  Recent observational and theoretical studies indicate that the stellar
initial mass function (IMF) varies systematically with the environment (star
formation rate - SFR, metallicity). Although the exact dependence of the IMF on
those properties is likely to change with improving observational constraints,
the reported trend in the shape of the IMF appears robust. We present the first
study aiming to evaluate the effect of the IMF variations on the measured
cosmic SFR density (SFRD) as a function of metallicity and redshift, $f_{\rm
SFR}$(Z,z). We also study the expected number and metallicity of white dwarf,
neutron star and black hole progenitors under different IMF assumptions.
Applying the empirically driven IMF variations described by the integrated
galactic IMF (IGIMF) theory, we correct $f_{\rm SFR}$(Z,z) obtained by
Chruslinska & Nelemans (2019) and find lower SFRD at high redshifts as well as
a higher fraction of metal-poor stars being formed. In the local Universe, our
calculation applying the IGIMF theory suggests more white dwarf and neutron
star progenitors in comparison with the universal IMF scenario, while the
number of black hole progenitors remains unaffected.
