Quasar-Cluster Associations and Gravitational Lensing by Large-Scale Matter Clumps

Motivated by the significant overdensity of background bright quasarsrecently detected behind the foreground clusters of galaxies on scale of $10$arcminutes, we have investigated the possibility of attributing thequasar-cluster associations to gravitational lensing by large-scale matterinhomogeneities. Based on the conventional lensing models, we have shown thatthe reported quasar overdensity is unlikely to be generated by cluster matteralone. The situation does not change even if all the clusters of galaxies whichfollow their spatial two-point correlation function are taken into account,while matter clumps on scale of $>20$ Mpc are also found to be unable toprovide the required mass surface density since their density contrast isstrictly limited by the anisotropy measurements of the cosmic backgroundradiation. Moreover, we have pointed out that the influence of a nonzerocosmological constant on the quasar-cluster associations is very minor. Weconclude that either the observed quasar number counts have been seriouslycontaminated by the magnification bias of matter inhomogeneities of theuniverse or there should exists some intercluster matter on scale of less than$\sim20$ Mpc, e.g. from cluster-galaxy correlation, whose mean cosmic densityis about an order of magnitude higher than that of clusters of galaxies.Comment: 14 pages, AASTEX, ApJ Lett., in pres