The Effect of Weak Gravitational Lensing on the Angular Distribution of Gamma-Ray Bursts

If Gamma-Ray Bursts (GRBs) are cosmologically distributed standard candles and are associated with the luminous galaxies, then the observed angular distribution of all GRBs is altered due to weak gravitational lensing of bursts by density inhomogeneities. The amplitude of the effect is generally small. For example, if the current catalogs extend to $z_{max}\sim 1$ and we live in a flat $\Omega=1$ Universe, the angular auto-correlation function of GRBs will be enhanced by $\sim 8\%$ due to lensing, on all angular scales. For an extreme case of $z_{max}= 1.5$ and ($\Omega$, $\Lambda$)=(0.2, 0.8), an enhancement of $\sim 33\%$ is predicted. If the observed distribution of GRBs is used in the future to derive power spectra of mass density fluctuations on large angular scales, the effect of weak lensing should probably be taken into account.