Production of high stellar-mass primordial black holes in trapped inflation

Abstract

Trapped inflation has been proposed to provide a successful inflation with a steep potential. We discuss the formation of primordial black holes in the trapped inflationary scenario. We show that primordial black holes are naturally produced during inflation with a steep trapping potential. In particular, we have given a recipe for an inflaton potential with which particle production can induce large non-Gaussian curvature perturbation that leads to the formation of high stellar-mass primordial black holes. These primordial black holes could be dark matter observed by the LIGO detectors through a binary black-hole merger. At the end, we have given an attempt to realize the required inflaton potential in the axion monodromy inflation, and discussed the gravitational waves sourced by the particle production.

Figures (5)

• Figure 1: Inflaton potential $V(\phi)$ with the dashed line denoting the quadratic term, $m^2\phi^2/2$. All dynamical variables in this figure and in the following figures are rescaled by the reduced Planck mass, $M_p=2.435\times 10^{18}$ GeV.
• Figure 2: Evolutions of $\phi$ (dashed line) and $\xi$ (solid line) as functions of e-foldings $N$ before the end of inflation. Inflation starts at $N_0\simeq 61$.
• Figure 3: Evolutions of the slow-roll parameters $\epsilon$ (solid line) and $\eta$ (dashed line) as functions of e-foldings $N$.
• Figure 4: Solid line is the total power spectrum of the curvature perturbation. The contribution induced by photon production is denoted by the dotted line and the vacuum contribution by the dashed line. The e-folding $N$ denotes the time when the $k$-mode leaves the horizon. The primordial black hole bound is the short-dashed line.
• Figure 5: Present spectral energy density of the gravitational waves associated with the production of $14 M_\odot$ PBHs. Also shown are the upper limits set by the pulsar timing array experiments EPTA, NANOGrav, and PPTA, as well as the projected SKA sensitivity.