First Frontier Field Constraints on the Cosmic Star Formation Rate Density at z ? 10?The Impact of Lensing Shear on Completeness of High-redshift Galaxy Samples

We search the complete Hubble Frontier Field data set of Abell 2744 and its parallel field for sources to further refine the evolution of the cosmic star formation rate density (SFRD) between and . We independently confirm two images of the recently discovered triply imaged source by Zitrin et al. and set an upper limit for similar galaxies with red colors of in the parallel field of Abell 2744. We utilize extensive simulations to derive the effective selection volume of Lyman-break galaxies at , both in the lensed cluster field and in the adjacent parallel field. Particular care is taken to include position-dependent lensing shear to accurately account for the expected sizes and morphologies of highly magnified sources. We show that both source blending and shear reduce the completeness at a given observed magnitude in the cluster, particularly near the critical curves. These effects have a significant, but largely overlooked, impact on the detectability of high-redshift sources behind clusters, and substantially reduce the expected number of highly magnified sources. The detections and limits from both pointings result in an SFRD which is consistent within the uncertainties with previous estimates at from blank fields. The combination of these new results with all other estimates is also consistent with a rapidly declining SFRD in the 170 Myr from to as predicted by cosmological simulations and dark-matter halo evolution in ?CDM. Once biases introduced by magnification-dependent completeness are accounted for, the full six cluster and parallel Frontier Field program will be an extremely powerful new data set to probe the evolution of the galaxy population at before the advent of the James Webb Space Telescope.