Counts of high-redshift GRBs as probes of primordial non-Gaussianities

We propose to use high-redshift long gamma-ray bursts (GRBs) as cosmological tools to constrain the amount of primordial non-Gaussianity in the density field. By using numerical, N-body, hydrodynamic, chemistry simulations of different cosmological volumes with various Gaussian and non-Gaussian models, we self-consistently relate the cosmic star formation rate density to the corresponding GRB rate. Assuming that GRBs are fair tracers of cosmic star formation, we find that positive local non-Gaussianities, described in terms of the non-linear parameter, fNL, might boost significantly the GRB rate at high redshift, z >> 6. Deviations with respect to the Gaussian case account for a few orders of magnitude if fNL similar to 1000, one order of magnitude for fNL similar to 100 and a factor of similar to 2 for fNL similar to 50. These differences are found only at large redshift, while at later times the rates tend to converge. Furthermore, a comparison between our predictions and the observed GRB data at z > 6 allows us to exclude large negative fNL, consistently with previous works. Future detections of any long GRB at extremely high redshift (z similar to 1520) could favour non-Gaussian scenarios with positive fNL. More stringent constraints require much larger high-z GRB complete samples, currently not available in the literature. By distinguishing the contributions to the GRB rate from the metal-poor Population III regime, and the metal-enriched Population III regime, we conclude that the latter is a more solid tracer of the underlying matter distribution, while the former is strongly dominated by feedback mechanisms from the first, massive, short-lived stars, rather than by possible non-Gaussian fluctuations. This holds quite independently of the assumed Population III initial mass function.