  In this work we explore the effects of adopting an initial mass function
(IMF) variable in time on the chemical evolution of the Galaxy. In order to do
that we adopt a chemical evolution model which assumes two main infall episodes
for the formation of the Galaxy. We study the effects on such a model of
different IMFs. First, we use a theoretical one based on the statistical
description of the density field arising from random motions in the gas. This
IMF is a function of time as it depends on physical conditions of the site of
star formation. We also investigate the behaviour of the model predictions
using other variable IMFs, parameterized as a function of metallicity. Our
results show that the theoretical IMF when applied to our model depends on time
but such time variation is important only in the early phases of the Galactic
evolution, when the IMF is biased towards massive stars. We also show that the
use of an IMF which is a stronger function of time does not lead to a good
agreement with the observational constraints suggesting that if the IMF varied
this variation should have been small. Our main conclusion is that the G-dwarf
metallicity distribution is best explained by infall with a large timescale and
a constant IMF, since it is possible to find variable IMFs of the kind studied
here, reproducing the G-dwarf metallicity but this worsens the agreement with
other observational constraints.
