We consider the inflationary model in which the inflaton $\varphi$ couples to another scalar field $\chi$ via the interaction $g^2(\varphi -{\varphi }_0{)}^2{\chi }^2$ with a small coupling constant $g$ ($g^2\sim {10}^{-7}$). We assume that there is a sequence of “trapping points” ${\varphi }_{0i}$ along the inflationary trajectory where particles of the $\chi$ field become massless and are rather effectively produced. We calculate the power spectrum of inflaton field fluctuations originating from a backreaction of $\chi$ particles produced using the Schwinger’s “in-in” formalism. We show that the primary curvature power spectrum produced by these backreaction effects is blue, which leads to a strong overproduction of primordial black holes (PBHs) in the subsequent radiation era.

• Received 12 April 2016

DOI:https://doi.org/10.1103/PhysRevD.94.023517