Accounting for Cosmic Variance in Studies of Gravitationally-Lensed High-Redshift Galaxies in the Hubble Frontier Field Clusters

Strong gravitational lensing provides a powerful means for studying faint galaxies in the distant universe. By magnifying the apparent brightness of background sources, massive clusters enable the detection of galaxies fainter than the usual sensitivity limit for blank fields. However, this gain in effective sensitivity comes at the cost of a reduced survey volume and, in this {\it Letter}, we demonstrate there is an associated increase in the cosmic variance uncertainty. As an example, we show that the cosmic variance uncertainty of the high redshift population viewed through the Hubble Space Telescope Frontier Field cluster Abell 2744 increases from ~35% at redshift z~7 to >~65% at z~10. Previous studies of high redshift galaxies identified in the Frontier Fields have underestimated the cosmic variance uncertainty that will affect the ultimate constraints on both the faint end slope of the high-redshift luminosity function and the cosmic star formation rate density, key goals of the Frontier Field program.