Primordial black hole constraints in cosmologies with early matter domination

Moduli fields, a natural prediction of any supergravity and superstring-inspired supersymmetry theory, may lead to a prolonged period of matter domination in the early Universe. This can be observationally viable provided the moduli decay early enough to avoid harming nucleosynthesis. If primordial black holes form, they would be expected to do so before or during this matter dominated era. We examine the extent to which the standard primordial black hole constraints are weakened in such a cosmology. Permitted mass fractions of black holes at formation are of order ${10}^{-8}$, rather than the usual ${10}^{-20}$ or so. If the black holes form from density perturbations with a power-law spectrum, its spectral index is limited to $n\lesssim 1.3$, rather than the $n\lesssim 1.25$ obtained in the standard cosmology.