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The Most Luminous z~9-10 Galaxy Candidates yet Found: The Luminosity Function, Cosmic Star-Formation Rate, and the First Mass Density Estimate at 500 Myr

[abridged] We present the discovery of four surprisingly bright (H_160 ~ 26 - 27 mag AB) galaxy candidates at z~9-10 in the complete HST CANDELS WFC3/IR GOODS-N imaging data, doubling the number of z~10 galaxy candidates that are known, just ~500 Myr after the Big Bang. Two similarly bright sources are also detected in a systematic re-analysis of the GOODS-S data set. Three of the four galaxies in GOODS-N are significantly detected at 4.5-6.2sigma in the very deep Spitzer/IRAC 4.5 micron data, as is one of the GOODS-S candidates. Furthermore, the brightest of our candidates (at z=10.2+-0.4) is robustly detected also at 3.6 micron (6.9sigma), revealing a flat UV spectral energy distribution with a slope beta=-2.0+-0.2, consistent with demonstrated trends with luminosity at high redshift. The abundance of such luminous candidates suggests that the luminosity function evolves more significantly in phi_* than in L_* at z>~8 with a higher number density of bright sources than previously expected. Despite the discovery of these luminous candidates, the cosmic star formation rate density for galaxies with SFR >0.7 M_sun/yr shows an order-of-magnitude increase in only 170 Myr from z ~ 10 to z ~ 8, consistent with previous results. Based on the IRAC detections, we derive galaxy stellar masses at z~10, finding that these luminous objects are typically 10^9 M_sun. The cosmic stellar mass density at z~10 is log10 rho_* = 4.7^+0.5_-0.8 M_sun Mpc^-3 for galaxies brighter than M_UV~-18. The remarkable brightness, and hence luminosity, of these z~9-10 candidates highlights the opportunity for deep spectroscopy to determine their redshift and nature, demonstrates the value of additional search fields covering a wider area to understand star-formation in the very early universe, and highlights the opportunities for JWST to map the buildup of galaxies at redshifts much earlier than z~10.