Limits on the high redshift growth of massive black holes

We place firm upper limits on the global accretion history of massive black holes at z>5 from the recently measured unresolved fraction of the cosmic X-ray background. The maximum allowed unresolved intensity observed at 1.5 keV implies a maximum accreted-mass density onto massive black holes of rho_acc < 1.4E4 M_sun Mpc^{-3} for z>5. Considering the contribution of lower-z AGNs, the value reduces to rho_acc < 0.66E4 M_sun Mpc^{-3}. The tension between the need for the efficient and rapid accretion required by the observation of massive black holes already in place at z>7 and the strict upper limit on the accreted mass derived from the X-ray background may indicate that black holes are rare in high redshift galaxies, or that accretion is efficient only for black holes hosted by rare galaxies.