INTEGRAL capabilities for faint Gamma-Ray Bursts

We discuss the INTEGRAL capabilities to detect a high redshift population of gamma-ray bursts (GRBs). First a simple comparison between other past or planned experiments (BATSE, SAX, HETE-2, Romer, Swift) and INTEGRAL instrumentation (IBIS, JEM-X) is shown. After this first view we will be focused on comparing the capabilities of the two most sensitive missions (INTEGRAL/IBIS and Swift) of detecting a further population of GRBs. We conclude that, if the GRB rate is proportional to the star formation rate, the capabilities of studying GRBs of INTEGRAL are complementary to the ones of missions like Swift and HETE-2, specially devoted to prompt localizations of GRBs. Whereas Swift and HETE-2 would detect a higher number of GRBs than INTEGRAL (~8 and ~22 more detections than IBIS and JEM-X respectively), INTEGRAL and specially IBIS would detect very high redshift (z > 15) GRBs, unreachable for Swift and HETE-2. This fact is very relevant for studying a population of GRBs further than z=15, which would be associated with the population III of stars. Therefore, the INTEGRAL mission (precisely IBIS) will be a very valuable tool to trace the primitive star formation rate at the early universe.