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Theoretical and indirect observational evidences suggest that stellar initialmass function (IMF) increases with redshift. On the other hand star formationrates (SFR) may be as high as 100 $M_{\odot}$ yr$^{-1}$ in star burst galaxies.These may lead to formation of massive clusters hence massive stars to make theintegrated galactic stellar initial mass function (IGIMF) top heavy (i.e.proportion of massive stars is higher than less massive stars). We investigatethe joint effect of evolving IMF and several measures of SFR in dependence ofgalaxy wide IMF. The resulting IGIMF have slopes $\alpha_{2,IGIMF}$ in the highmass regime, which is highly dependent on the minimum mass of the embeddedcluster ($M_{ecl,min}$), star formation rates and mass spectrum indices ofembedded clusters (viz. $\beta$). It is found that for z $\sim$ 0 - 2,$\alpha_{2,IGIMF}$ becomes steeper (i.e. bottom heavy), for z $\sim$ 2 - 4,$\alpha_{2,IGIMF}$ becomes flatter (i.e. top heavy ) and from z $\sim$ 4onwards $\alpha_{2,IGIMF}$ becomes again steeper. The effects are faster forhigher values of $\beta$. $\alpha_{2,IGIMF}$ is flatter also for higher valuesof $M_{ecl,min}$. All these effects might be counted for the joint effect ofincreasing temperature of the ambient medium as well as varying SFR withincreasing redshift.

Cosmic history of integrated galactic stellar initial mass function : a simulation study