CONSTRAINTS ON THE DENSITY OF PERTURBATION SPECTRUM FROM PRIMORDIAL BLACK-HOLES

We reexamine the constraints on the density perturbation spectrum, inc luding its spectral index n, from the production of primordial black h oles. The standard cosmology, where the Universe is radiation dominate d from the end of inflation up until the recent past, was studied by C arr, Gilbert, and Lidsey; we correct two errors in their derivation an d find a significantly stronger constraint than they did: n less than or similar to 1.25 rather than their 1.5. We then consider an alternat ive cosmology in which a second period of inflation, known as thermal inflation and designed to solve additional relic overdensity problems, occurs at a lower-energy scale than the main inflationary period. In that case, the constraint weakens to n less than or similar to 1.3, an d thermal inflation also leads to a ''missing mass'' range 10(18) g le ss than or similar to M less than or similar to 10(26) g in which prim ordial black holes cannot form. Finally, we discuss the effect of allo wing for the expected non-Gaussianity in the density perturbations pre dicted by Bullock and Primack, which can weaken the constraints furthe r by up to 0.05. [S0556-2821(97)04022-8].