Black hole formation and slow-roll inflation

Black hole formation may occur if the spectrum of the curvature perturbation ζ increases strongly as the scale decreases. As no such increase is observed on cosmological scales, black hole formation requires strongly positive running n ' of the spectral index n , though the running might only kick in below the 'cosmological scales' probed by the cosmic microwave background anisotropy and galaxy surveys. A concrete and well-motivated way of producing this running is through the running mass model of slow-roll inflation. We obtain a new observational bound n '<0.026 on the running provided by this model, improving an earlier result by a factor 2. We also discuss black hole production in more general scenarios. We show that the usual conditions and are enough to derive the spectrum , the introduction of higher order parameters ξ 2 etc being optional.