  The observed stellar initial mass function (IMF) appears to vary, becoming
bottom-heavy in the centres of the most massive, metal-rich early-type
galaxies. It is still unclear what physical processes might cause this IMF
variation. In this paper, we demonstrate that the abundance of deuterium in the
birth clouds of forming stars may be important in setting the IMF. We use
models of disc accretion onto low-mass protostars to show that those forming
from deuterium-poor gas are expected to have zero-age main sequence masses
significantly lower than those forming from primordial (high deuterium
fraction) material. This deuterium abundance effect depends on stellar mass in
our simple models, such that the resulting IMF would become bottom-heavy - as
seen in observations. Stellar mass loss is entirely deuterium-free and is
important in fuelling star formation across cosmic time. Using the EAGLE
simulation we show that stellar mass loss-induced deuterium variations are
strongest in the same regions where IMF variations are observed: at the centres
of the most massive, metal-rich, passive galaxies. While our analysis cannot
prove that the deuterium abundance is the root cause of the observed IMF
variation, it sets the stage for future theoretical and observational attempts
to study this possibility.
