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

If Gamma-Ray Bursts (GRBs) are cosmologically distributed standard candlesand are associated with the luminous galaxies, then the observed angulardistribution of all GRBs is altered due to weak gravitational lensing of burstsby density inhomogeneities. The amplitude of the effect is generally small. Forexample, if the current catalogs extend to $z_{max}\sim 1$ and we live in aflat $\Omega=1$ Universe, the angular auto-correlation function of GRBs will beenhanced by $\sim 8\%$ due to lensing, on all angular scales. For an extremecase 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 thefuture to derive power spectra of mass density fluctuations on large angularscales, the effect of weak lensing should probably be taken into account.Comment: 16 pages, 2 figures, uses AASTEX macros, aasms4.sty included, accepted to Ap