Angular Distribution of Gamma-Ray Bursts and Weak Lensing

We investigate whether gamma-ray bursts (GRBs) from the current BATSE catalog have been affected by weak lensing by the nearby large-scale structure. The redshift distribution of GRBs is believed to be broad, extending to z ~ 5, so most events can be assumed to be at large redshifts and hence subject to weak lensing, which would betray itself as projected (anti)correlations between GRB events and galaxies or clusters that trace the intervening mass. Given the observed distribution of GRBs in fluence f, and statistical positional error e, we predict that most subsets drawn from the BATSE catalog will be anticorrelated with the foreground structure because of weak lensing, i.e., will show negative magnification bias. We find that GRBs are indeed anticorrelated with the Automatic Plate Measuring Facility (APM) galaxies (z ~ 0.2-0.3) in the sense that galaxy density in circles of radii 1°-1.°5 (15-20 h-1 Mpc at z ~ 0.3) centered on e ≲ 1° GRBs is about 10% lower than expected from a random distribution; the significance of GRB-APM anticorrelations reaches 99.7%. Cross-correlation between GRBs and distant, rich Abell-Corwin-Olowin clusters is also negative. Standard cosmological models with Ωm ~ 0.3, ΩΛ ~ 0.7, and matter distribution on large scales following observed APM galaxy distribution with the biasing parameter of around 1 are not able to reproduce our GRB-APM anticorrelations. We propose a speculative model that does account for these anticorrelations, as well as positive correlations found previously, between quasi-stellar objects and APM galaxies. We briefly discuss if the proposed scheme is in conflict with observations of cosmic microwave background, galaxy surveys, cosmic velocity flows, and weak shear lensing.