Moduli constraints on primordial black holes

The amount of late decaying massive particles (e.g., gravitinos, moduli) produced in the evaporation of primordial black holes (PBHs) of mass $\Mbh\la10^9 $g is calculated. Limits imposed by big-bang nucleosynthesis on the abundance of these particles are used to constrain the initial PBH mass fraction $\beta$ (ratio of PBH energy density to critical energy density at formation), as: $\beta\la 5\times10^{-19} (\xp/6 10^{-3})^{-1} (\Mbh/10^9 {\rm g})^{-1/2} (\bar{\Yp}/10^{-14})$; $\xp$ is the fraction of PBH luminosity going into gravitinos or moduli, $\bar{\Yp}$ is the upper bound imposed by nucleosynthesis on the number density to entropy density ratio of gravitinos or moduli. This notably implies that such PBHs should never come to dominate the cosmic energy density.