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.

20 pages, 15 figures. Accepted for publication in MNRAS. Fig. 3 is new relative to the submitted version, showing the dependence of IMF slope radial gradients on (global) central stellar velocity dispersion