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A debate is emerging regarding the recent inconsistent results of differentstudies for the Cosmic Star Formation Rate Density (CSFRD) at high-z. We employUV and IR datasets to investigate the star formation rate function (SFRF) at${\rm z \sim 0-9}$. We find that the SFRFs derived from the dust corrected${\rm UV}$ (${\rm UV_{corr}}$) data contradict those from IR on some key issuessince they are described by different distributions (Schechter vs double-powerlaw), imply different physics for galaxy formation (${\rm UV_{corr}}$ datasuggest a SFR limit/strong mechanism that diminish the number density of highstar forming systems with respect IR) and compare differently with the stellarmass density evolution obtained from SED fitting (${\rm UV_{corr}}$ is inagreement, while IR in tension up to 0.5 dex). However, both tracers agree on aconstant CSFRD evolution at ${\rm z \sim 1-4}$ and point to a plateau insteadof a peak. In addition, using both indicators we demonstrate that the evolutionof the {\it observed} CSFRD can be described by only {\bf 2} parameters and afunction that has the form of a Gamma distribution (${\bf \Gamma(a,bt)}$). Incontrast to previous parameterizations used in the literature our frameworkconnects the parameters to physical properties like the star formation ratedepletion time and cosmic baryonic gas density. The build up of stellar massoccurs in $\Gamma(a,bt)$ distributed steps and is the result of gas consumptionup to the limit that there is no eligible gas for SF at t = ${\rm \infty}$,resulting to a final cosmic stellar mass density of $\sim 0.5 \times 10^9 \,{\rm \frac{M_{\odot}}{Mpc^3}}$.

astrophysical journal/the astrophysical journal

The observed cosmic star formation rate density has an evolution which  resembles a {\Gamma}(a, bt) distribution and can be described successfully by  only 2 parameters