  The stellar initial mass function (IMF) plays a crucial role in determining
the number of surviving stars in galaxies, the chemical composition of the
interstellar medium, and the distribution of light in galaxies. A key unsolved
question is whether the IMF is universal in time and space. Here we use
state-of-the-art results of stellar evolution to show that the IMF of our
Galaxy made a transition from an IMF dominated by massive stars to the
present-day IMF at an early phase of the Galaxy formation. Updated results from
stellar evolution in a wide range of metallicities have been implemented in a
binary population synthesis code, and compared with the observations of
carbon-enhanced metal-poor (CEMP) stars in our Galaxy. We find that applying
the present-day IMF to Galactic halo stars causes serious contradictions with
four observable quantities connected with the evolution of AGB stars.
Furthermore, a comparison between our calculations and the observations of CEMP
stars may help us to constrain the transition metallicity for the IMF which we
tentatively set at [Fe/H] = -2. A novelty of the current study is the inclusion
of mass loss suppression in intermediate-mass AGB stars at low-metallicity.
This significantly reduces the overproduction of nitrogen-enhanced stars that
was a major problem in using the high-mass star dominated IMF in previous
studies. Our results also demonstrate that the use of the present day IMF for
all time in chemical evolution models results in the overproduction of Type I.5
supernovae. More data on stellar abundances will help to understand how the IMF
has changed and what caused such a transition.
