Cluster gravitational lensing surveys like the Hubble Space Telescope Frontier Fields survey will detect distant galaxies 10-50 times fainter than any yet discovered. Using these surveys to measure the luminosity function of such faint, distant galaxies, however, requires that magnification maps built from the constraints of strongly-lensed images be accurate. For models that assume the cluster and nearby (correlated) structures are the only significant sources of lensing, a potential source of error in these maps comes from the fact that light rays also suffer weak deflections by uncorrelated large-scale structure along the line-of-sight, i.e. cosmic weak lensing (CWL). To demonstrate the magnitude of this effect, we calculate the magnification change which results when the same cluster-lens is placed along different lines of sight. Using a simple density profile for a cluster-lens at z~0.3-0.5 and the power spectrum of the matter density fluctuations responsible for CWL, we show that the typical magnifications of ~5(10) of sources at z=6-10 can differ by ~10-20(20-30)% from one line-of-sight to another. However, these fluctuations rise to greater than order unity near critical curves, indicating that CWL tends to make its greatest contribution to the most magnified images. We conclude that the neglect of CWL in determining the intrinsic luminosities of highly-magnified galaxies may introduce errors significant enough to warrant further effort to include this contribution in cluster-lens modeling. We suggest that methods of modeling CWL in galaxy-strong-lensing systems should be generalized to cluster-lensing systems.
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