Gamma Ray Bursts ( GRBs ) and galaxies at high redshift represent complementary probes of the star formation history of the Universe .
In fact , both the GRB rate and the galaxy luminosity density are connected to the underlying star formation .
Here , we combine a star formation model for the evolution of the galaxy luminosity function from z = 0 to z = 10 with a metallicity-dependent efficiency for GRB formation to simultaneously predict the comoving GRB rate .
Our model sheds light on the physical origin of the empirical relation often assumed between GRB rate and luminosity density-derived star formation rate : \dot { n } _ { GRB } ( z ) = \varepsilon ( z ) \times \dot { \rho } ^ { * } _ { obs } ( z ) , with \varepsilon ( z ) \propto ( 1 + z ) ^ { 1.2 } .
At z \lesssim 4 , \varepsilon ( z ) is dominated by the effects of metallicity evolution in the GRB efficiency .
Our best-fitting model only requires a moderate preference for low-metallicity , that is a GRB rate per unit stellar mass about four times higher for \log { ( Z / Z _ { \odot } ) } < -3 compared to \log { ( Z / Z _ { \odot } ) } > 0 .
Models with total suppression of GRB formation at \log { ( Z / Z _ { \odot } ) } \gtrsim 0 are disfavoured .
At z \gtrsim 4 , most of the star formation happens in low-metallicity hosts with nearly saturated efficiency of GRB production per unit stellar mass .
However at the same epoch , galaxy surveys miss an increasing fraction of the predicted luminosity density because of flux limits , driving an accelerated evolution of \varepsilon ( z ) compared to the empirical power-law fit from lower z .
Our findings are consistent with the non-detections of GRB hosts in ultradeep imaging at z > 5 , and point toward current galaxy surveys at z > 8 only observing the top 15 - 20 \% of the total luminosity density .