Cosmic SFH plotted for the universal (dashed lines) and non-universal (solid lines) IMF case using the high-Z extreme f_SFR(Z, z) (thin lines) and the f_SFR(Z, z) with the same MZR and SFMR, but with the slope of the low-mass end of the GSMF allowed to steepen with redshift as discussed in ChN19 (thick lines). For the high-Z extreme example we also show the cosmic SFH obtained using the IGIMF2 (light blue) or IGIMF3 (dark blue) non-universal IMF model. The former is slightly higher, but the difference is negligible.