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 dataset of Abell 2744 and its parallel field for z~10 sources to further refine the evolution of the cosmic star-formation rate density (SFRD) at z>8. We independently confirm two images of the recently discovered triply-imaged z~9.8 source by Zitrin et al. (2014) and set an upper limit for similar z~10 galaxies with red colors of J_125-H_160>1.2 in the parallel field of Abell 2744. We utilize extensive simulations to derive the effective selection volume of Lyman-break galaxies at z~10, 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 a SFRD which is higher by 0.4+-0.4 dex than previous estimates at z~10 from blank fields. Nevertheless, the combination of these new results with all other estimates remain consistent with a rapidly declining SFRD in the 170 Myr from z~8 to z~10 as predicted by cosmological simulations and dark-matter halo evolution in LambdaCDM. 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 dataset to probe the evolution of the galaxy population at z>8 before the advent of the JWST.