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We present the comprehensive analyses of faint dropout galaxies up to$z\sim10$ with the first full-depth data set of Abell 2744 lensing cluster andparallel fields observed by the Hubble Frontier Fields (HFF) program. Weidentify $54$ dropouts at $z\sim5-10$ in the HFF fields, and enlarge the sizeof $z\sim9$ galaxy sample obtained to date. Although the number of highlymagnified ($\mu\sim10$) galaxies is small due to the tiny survey volume ofstrong lensing, our study reaches the galaxies' intrinsic luminositiescomparable to the deepest-field HUDF studies. We derive UV luminosity functionswith these faint dropouts, carefully evaluating the combination ofobservational incompleteness and lensing effects in the image plane byintensive simulations including magnification, distortion, and multiplicationof images, with the evaluations of mass model dependences. Our results confirmthat the faint-end slope, $\alpha$, is as steep as $-2$ at $z\sim6-8$, andstrengthen the evidence of the rapid decrease of UV luminosity densities,$\rho_\mathrm{UV}$, at $z>8$ from the large $z\sim9$ sample. We examine whetherthe rapid $\rho_\mathrm{UV}$ decrease trend can reconcile with the largeThomson scattering optical depth, $\tau_\mathrm{e}$, measured by CMBexperiments allowing a large space of free parameters such as average ionizingphoton escape fraction and stellar-population dependent conversion factor. Noparameter set can reproduce both the rapid $\rho_\mathrm{UV}$ decrease and thelarge $\tau_\mathrm{e}$. It is possible that the $\rho_\mathrm{UV}$ decreasemoderates at $z\gtrsim11$, that the free parameters significantly evolvetowards high-$z$, or that there exist additional sources of reionization suchas X-ray binaries and faint AGNs.

Hubble Frontier Fields First Complete Cluster Data: Faint Galaxies at $z\sim 5-10$ for UV Luminosity Functions and Cosmic Reionization