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We investigate the evolution of the galaxy Star Formation Rate Function(SFRF) and Cosmic Star Formation Rate Density (CSFRD) of $z\sim 1-4 $ galaxies,using cosmological Smoothed Particle Hydrodynamic (SPH) simulations and acompilation of UV, IR and H$\alpha$ observations. These tracers representdifferent populations of galaxies with the IR light being a probe of objectswith high star formation rates and dust contents, while UV and H$\alpha$observations provide a census of low star formation galaxies where mildobscuration occurs. We compare the above SFRFs with the results of SPHsimulations run with the code {\small{P-GADGET3(XXL)}}. We focus on the role offeedback from Active Galactic Nuclei (AGN) and supernovae in form of galacticwinds. The AGN feedback prescription that we use decreases the simulated CSFRDat $z < 3$ but is not sufficient to reproduce the observed evolution at higherredshifts. We explore different wind models and find that the key factor forreproducing the evolution of the observed SFRF and CSFRD at $z \sim1-4$ is thepresence of a feedback prescription that is prominent at high redshifts ($z \ge4$) and becomes less efficient with time. We show that variable galactic windswhich are efficient at decreasing the SFRs of low mass objects are quitesuccessful in reproducing the observables.

The evolution of the star formation rate function and cosmic star formation rate density of galaxies at $z \sim 1-4$