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.
Contrary to the conventional wisdom, we find that it is plausible to generate primordial magnetic seed fields via spinodal instability efficiently during cosmic inflation provided that a fast-roll stage is involved before the inflaton entering into the slow-roll phase. Moreover, the primordial magnetic field produced in such a mechanism can be used to constrain the low quadrupole moment of Cosmic Microwave Background.
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