Trapping effects in inflation: blue spectrum at small scales

TL;DR

This paper studies how interactions during inflation can produce a blue-tilted power spectrum at small scales, potentially causing overproduction of primordial black holes due to particle trapping effects.

Contribution

It introduces a model where inflaton coupling to another scalar field causes trapping points, leading to a blue spectrum from backreaction effects, a novel mechanism in inflationary cosmology.

Findings

Power spectrum becomes blue at small scales due to trapping effects.

Significant overproduction of primordial black holes predicted.

Backreaction from produced particles dominates inflaton fluctuations.

Abstract

We consider the inflationary model in which the inflaton $\phi$ couples to another scalar field $\chi$ via the interaction $g^2(\phi-\phi_0)^2\chi^2$ with a small coupling constant $g$ ($g^2 \sim 10^{-7}$). We assume that there is a sequence of "trapping points" $\phi_{0i}$ along the inflationary trajectory where particles of $\chi$-field become massless and are rather effectively produced. We calculate the power spectrum of inflaton field fluctuations originated 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 subsequent radiation era.