We measure the star formation rate ( SFR ) as a function of redshift z up to z \approx 4.5 , based on B , I and ( I+B ) selected galaxy catalogues from the FORS Deep Field ( FDF ) and the K-selected catalogue from the GOODS-South field .
Distances are computed from spectroscopically calibrated photometric redshifts accurate to \Delta z / ( z _ { spec } +1 ) \leq 0.03 for the FDF and \leq 0.056 for the GOODS-South field .
The SFRs are derived from the luminosities at 1500 Å .
We find that the total SFR estimates derived from B , I and I+B catalogues agree very well ( \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt \hbox { $ < $ } } 0.1 dex ) while the SFR from the K catalogue is lower by \approx 0.2 dex .
We show that the latter is solely due to the lower star-forming activity of K-selected intermediate and low luminosity ( L < L _ { \ast } ) galaxies .
The SFR of bright ( L > L _ { \ast } ) galaxies is independent of the selection band , i.e . the same for B , I , ( I+B ) , and K-selected galaxy samples .
At all redshifts , luminous galaxies ( L > L _ { \ast } ) contribute only \sim \frac { 1 } { 3 } to the total SFR .
There is no evidence for significant cosmic variance between the SFRs in the FDF and GOODs-South field , \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt \hbox { $ < $ } } 0.1 dex , consistent with theoretical expectations .
The SFRs derived here are in excellent agreement with previous measurements provided we assume the same faint-end slope of the luminosity function as previous works ( \alpha \sim - 1.6 ) .
However , our deep FDF data indicate a shallower slope of \alpha = -1.07 , implying a SFR lower by \approx 0.3 dex .
We find the SFR to be roughly constant up to z \approx 4 and then to decline slowly beyond , if dust extinctions are assumed to be constant with redshift .