Galaxy formation with cold gas accretion and evolving stellar initial
  mass function
  The evolution of the galaxy stellar mass function is especially useful to
test the current model of galaxy formation. Observational data have revealed a
few inconsistencies with predictions from the $\Lambda {\rm CDM}$ model. For
example, most massive galaxies have already been observed at very high
redshifts, and they have experienced only mild evolution since then. In
conflict with this, semi-analytical models of galaxy formation predict an
insufficient number of massive galaxies at high redshift and a rapid evolution
between redshift 1 and 0 . In addition, there is a strong correlation between
star formation rate and stellar mass for star-forming galaxies, which can be
roughly reproduced with the model, but with a normalization that is too low at
high redshift. Furthermore, the stellar mass density obtained from the integral
of the cosmic star formation history is higher than the measured one by a
factor of 2. In this paper, we study these issues using a semi-analytical model
that includes: 1) cold gas accretion in massive halos at high redshift; 2)
tidal stripping of stellar mass from satellite galaxies; and 3) an evolving
stellar initial mass function (bottom-light) with a higher gas recycle
fraction. Our results show that the combined effects from 1) and 2) can predict
sufficiently massive galaxies at high redshifts and reproduce their mild
evolution at low redshift, While the combined effects of 1) and 3) can
reproduce the correlation between star formation rate and stellar mass for
star-forming galaxies across wide range of redshifts. A bottom-light/top-heavy
stellar IMF could partly resolve the conflict between the stellar mass density
and cosmic star formation history.
