Bounds from primordial black holes with a near critical collapse initial mass function - art. no. 103510

Recent numerical evidence suggests that a mass spectrum of primordial black holes (PBHs) is produced as a consequence of near critical gravitational c ollapse. Assuming that these holes formed from the initial density perturba tions seeded by inflation, we calculate model independent upper bounds on t he mass variance at the reheating temperature by requiring that the mass de nsity does not exceed the critical density and the photon emission does not exceed current diffuse gamma-ray measurements. We then translate these res ults into bounds on the spectral index n by utilizing the COBE data to norm alize the mass variance at large scales, assuming a constant power law, and scale this result to the reheating temperature. We find that our bounds on n differ substantially (delta n > 0.05) from those calculated using initia l mass functions derived under the assumption that the black hole mass is p roportional to the horizon mass at the collapse epoch. We also find a chang e in the shape of the diffuse gamma-ray spectrum which results from the Haw king radiation. Finally, we study the impact of a nonzero cosmological cons tant and find that the bounds on n are strengthened considerably if the uni verse is indeed vacuum-energy dominated today. [S0556-2821(99)07620-1].