  Recent spatially-resolved observations of massive early-type galaxies (ETGs)
have uncovered evidence for radial gradients of the stellar initial mass
function (IMF), ranging from super-Salpeter IMFs in the centre to Milky
Way-like beyond the half-light radius, $r_e$. We compare these findings with
our new cosmological, hydrodynamical simulations based on the EAGLE model that
self-consistently vary the IMF on a per-particle basis such that it becomes
either bottom-heavy (LoM-50) or top-heavy (HiM-50) in high-pressure
environments. These simulations were calibrated to reproduce inferred IMF
variations such that the IMF becomes "heavier" due to either excess dwarf stars
or stellar remnants, respectively, in galaxies with increasing stellar velocity
dispersion. In agreement with observations, both simulations produce negative
radial IMF gradients, transitioning from high to low excess mass-to-light ratio
(MLE) at around $r_e$. We find negative metallicity radial gradients for both
simulations, but positive and flat [Mg/Fe] gradients in LoM-50 and HiM-50,
respectively. Measured in radial bins, the MLE increases strongly with local
metallicity for both simulations, in agreement with observations. However, the
local MLE increases and decreases with local [Mg/Fe] in LoM-50 and HiM-50,
respectively. These qualitative differences can be used to break degeneracies
in the manner with which the IMF varies in these high-mass ETGs. At $z=2$, we
find that the MLE has a higher and lower normalization for bottom- and
top-heavy IMF variations, respectively. We speculate that a hybrid of our LoM
and HiM models may be able to reconcile observed IMF diagnostics in
star-forming galaxies and ETGs.
