It has recently been suggested that cosmologically significant numbers of black holes could form during a first-order QCD phase transition .
Further , it has been asserted that these black holes would have masses corresponding naturally to the inferred mass ( \sim 1 M _ { \odot } ) of the MACHOs responsible for the observed gravitational microlensing events .
In this model , the underlying spectrum of primordial density perturbations provides the fluctuations that give rise to black holes at the epoch of the QCD transition .
We employ a simplified model to estimate the reduction in the critical overdensity of a horizon-sized primordial perturbation required for collapse to a black hole .
We find that a first-order QCD transition does indeed produce a sharp peak in the black hole mass spectrum , but that this peak corresponds to the horizon mass at an epoch somewhat earlier than the cosmological transition itself .
Assuming a COBE normalized primordial density perturbation spectrum with constant spectral index , for the black holes so produced to be cosmologically significant would require an extremely finely tuned “ blue ” primordial density perturbation spectrum .
Specifically , in the context of our simplified model , a spectral index in the range n = 1.37 - 1.42 corresponds to the range \Omega \sim 10 ^ { -5 } -10 ^ { 3 } of the black hole contribution to the present-day density parameter .