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 \sim 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 BATSE Catalog will be anti-correlated with the foreground structure due to weak lensing , i.e .
will show negative magnification bias .
We find that GRBs are indeed anti-correlated with the APM galaxies ( z \sim 0.2 - 0.3 ) in the sense that galaxy density in circles of radii 1 ^ { \circ } -1.5 ^ { \circ } ( 15 - 20 ~ { } h ^ { -1 } Mpc at z \sim 0.3 ) centered on e \hbox { \hbox to 0.0 pt { \raise 1.8275 pt \hbox { $ < $ } } \lower 2.795 pt \hbox { $ \sim$ } } % 1 ^ { \circ } GRBs is about 10 % lower than expected from a random distribution ; the significance of GRB-APM anti-correlations reaches 99.7 % .
Cross-correlation between GRBs and distant rich Abell-Corwin-Olowin clusters is also negative .
Standard cosmological models with \Omega _ { m } \sim 0.3 , \Omega _ { \Lambda } \sim 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 anti-correlations .
We propose a speculative model that does account for these anti-correlations as well as positive correlations found previously , between QSOs 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 .