Generating primordial black holes via hilltop-type inflation models

Abstract

It has been shown that black holes would have formed in the early Universe if, on any given scale, the spectral amplitude of the cosmic microwave background exceeds ${\mathcal{P}}_{\ensuremath{\zeta}}\ensuremath{\sim}{10}^{\ensuremath{-}4}$. This value is within the bounds allowed by astrophysical phenomena for the small scale spectrum of the cosmic microwave background, corresponding to scales which exit the horizon at the end of slow-roll inflation. Previous work by Kohri et al. (2007) showed that for black holes to form from a single field model of inflation, the slope of the potential at the end of inflation must be flatter than it was at horizon exit. In this work we show that a phenomenological hilltop model of inflation, satisfying the Kohri et al. criteria, could lead to the production of black holes, if the power of the inflaton self-interaction is less than or equal to 3, with a reasonable number or $e$-folds. We extend our analysis to the running mass model, and confirm that this model results in the production of black holes, and by using the latest WMAP year 5 bounds on the running of the spectral index, and the black hole constraint we update the results of Leach et al. (2000) excluding more of parameter space.