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We explore the assumption, widely used in many astrophysical calculations,that the stellar initial mass function (IMF) is universal across all galaxies.By considering both a canonical Salpeter-like IMF and a non-universal IMF, weare able to compare the effect of different IMFs on multiple observables andderived quantities in astrophysics. Specifically, we consider a non-universalIMF which varies as a function of the local star formation rate, and explorethe effects on the star formation rate density (SFRD), the extragalacticbackground light, the supernova (both core-collapse and thermonuclear) rates,and the diffuse supernova neutrino background. Our most interesting result isthat our adopted varying IMF leads to much greater uncertainty on the SFRD at$z \approx 2-4$ than is usually assumed. Indeed, we find a SFRD (inferred usingobserved galaxy luminosity distributions) that is a factor of $\gtrsim 3$ lowerthan canonical results obtained using a universal Salpeter-like IMF. Secondly,the non-universal IMF we explore implies a reduction in the supernovacore-collapse rate of a factor of $\sim2$, compared against a universal IMF.The other potential tracers are only slightly affected by changes to theproperties of the IMF. We find that currently available data do not provide aclear preference for universal or non-universal IMF. However, improvements tomeasurements of the star formation rate and core-collapse supernova rate atredshifts $z \gtrsim 2$ may offer the best prospects for discernment.

Non-Universal Stellar Initial Mass Functions: Large Uncertainties in Star Formation Rates at $z\approx 2-4$ and Other Astrophysical Probes