2012MNRAS.426.2078M

We propose to use high-redshift long γ-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, f_NL, 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 f_NL ∼ 1000, one order of magnitude for f_NL ∼ 100 and a factor of ∼ 2 for f_NL ∼ 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 f_NL, consistently with previous works. Future detections of any long GRB at extremely high redshift (z ∼ 15–20) could favour non-Gaussian scenarios with positive f_NL. 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 II–I 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.