Single-field inflation, anomalous enhancement of superhorizon fluctuations, and non-Gaussianity in primordial black hole formation

TL;DR

This work demonstrates that a single-field Coleman–Weinberg potential can realize double inflation, producing an anomalous growth of curvature perturbations at the onset of the second inflation and a strongly peaked small-scale power spectrum that enables primordial black hole formation. The authors solve the full perturbation evolution, quantify PBH abundances via the Press–Schechter framework, and show that non-Gaussian corrections from cubic interactions are numerically small. A parameter search identifies regimes where PBHs can account for a significant fraction of dark matter, while predicting observable induced gravitational waves in some cases. The results highlight a concrete mechanism linking high-energy inflationary dynamics to PBH production and possible GW signatures, with implications for early-universe phenomenology and dark matter.

Abstract

We show a text-book potential for single-field inflation, namely, the Coleman-Weinberg model can induce double inflation and formation of primordial black holes (PBHs), because fluctuations that leave the horizon near the end of first inflation are anomalously enhanced at the onset of second inflation when the time-dependent mode turns to a growing mode rather than a decaying mode. The mass of PBHs produced in this mechanism lies in several discrete ranges depending on the model parameters. We also calculate the effects of non-Gaussian statistics due to higher-order interactions on the abundance of PBHs, which turns out to be small.

Figures (6)

• Figure 1: The evolution of Hubble parameter(left) and the inflaton(right) with the values of the parameters $(\lambda,~v)=(5.4\times10^{-14},~0.355139M_{G})$. $a_i$ is a value of scale factor at the initial time.
• Figure 2: The evolution of slow-roll parameters with the values of the parameters $(\lambda,~v)=(5.4\times10^{-14},~0.355139M_{G})$.
• Figure 3: Power spectrum of curvature perturbation (solid line). This spectrum is calculated under the parameters $(\lambda,~v)=(5.4\times10^{-14},~0.355139M_{G})$. We show also a power spectrum estimated by using the formula (\ref{['eq:srps']}), which is used for a slow-roll inflation model (dashed line).
• Figure 4: PBH abundance with some values of $J_{\text{peak}}$. The values of $J_{\text{peak}}$ are $-0.1,-0.01,0,0.01,0.1$ from below.
• Figure 5: PBH abundance $\beta$ as a function of mass corresponding to the scale of the peak $M_{\text{peak}}$ associated with the values of parameter $v=0.2666694M_{G}-0.2666745M_{G}$ (solid line). The constraints on PBH abundance are also depicted.