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We study the evolution of the star formation rate function (SFRF) of massive ( M  ★  &gt; 10 10  M ⊙ ) galaxies over the 0.4 &lt;  z  &lt; 1.8 redshift range and its implications for our understanding of the physical processes responsible for galaxy evolution. We use multiwavelength observations included in the Great Observatories Origins Deep Survey‐Multiwavelength Southern Infrared Catalog (GOODS‐MUSIC) catalogue, which provides a suitable coverage of the spectral region from 0.3 to 24 m and either spectroscopic or photometric redshifts for each object. Individual SFRs have been obtained by combining ultraviolet and 24‐m observations, when the latter were available. For all other sources a ‘spectral energy distribution (SED) fitting’ SFR estimate has been considered. We then define a stellar mass limited sample, complete in the  M  ★  &gt; 10 10  M ⊙  range and determine the SFRF using the 1/ V  max  algorithm. We thus define simulated galaxy catalogues based on the predictions of three different state‐of‐the‐art semi‐analytical models (SAMs) of galaxy formation and evolution, and compare them with the observed SFRF. We show that the theoretical SFRFs are well described by a double power law functional form and its redshift evolution is approximated with high accuracy by a pure evolution of the typical SFR (SFR ★ ). We find good agreement between model predictions and the high‐SFR end of the SFRF, when the observational errors on the SFR are taken into account. However, the observational SFRF is characterized by a double‐peaked structure, which is absent in its theoretical counterparts. At  z  &gt; 1.0 the observed SFRF shows a relevant density evolution, which is not reproduced by SAMs, due to the well‐known overprediction of intermediate‐mass galaxies at  z ∼ 2. SAMs are thus able to reproduce the most intense SFR events observed in the GOODS‐MUSIC sample and their redshift distribution. At the same time, the agreement at the low‐SFR end is poor: all models overpredict the space density of SFR ∼ 1 M ⊙  yr −1  and no model reproduces the double‐peaked shape of the observational SFRF. If confirmed by deeper infrared observations, this discrepancy will provide a key constraint on theoretical modelling of star formation and stellar feedback.

On the evolution of the star formation rate function of massive galaxies: constraints at from the GOODS‐MUSIC catalogue