Primordial black holes and Scalar-Induced Gravitational Waves formed by inflation potential with non-trivial characteristics

TL;DR

This work investigates whether primordial black holes (PBHs) can arise from enhanced small-scale perturbations in inflationary models by introducing a local Lorentzian-type coupling to standard potentials (Starobinsky and KKLT). The coupling locally breaks slow-roll, triggering a transient ultra-slow-roll phase that amplifies the power spectrum $P_S(k)$ on small scales while keeping large-scale CMB observables intact. This amplification yields calculable PBH abundances in specific mass windows and generates scalar-induced gravitational waves (SIGWs) with characteristic frequency peaks that may be detectable by current or future gravitational wave experiments. The approach is shown to be universal across the chosen potentials and can be extended (e.g., double-coupling) to produce multiple PBH and SIGW features, all within existing observational constraints.

Abstract

The formation of primordial black holes (PBHs) generally requires large density perturbations, which is widely supported by researchers. This paper studies the local coupling properties of the Starobinsky potential and KKLT potential by introducing a linear Lorentzian-type coupling, which locally breaks the slow roll conditions. We found that both positive and negative coupling can form a considerable abundance of PBH. Additionally, we also studied the scalar-induced gravitational waves (SIGWs) generated by this model.

Figures (22)

• Figure 1: The Starobinsky potential with local positive coupling corresponds to Eq. (\ref{['Potential']}), and the parameter values correspond to Eq. (\ref{['CS1']}), where the coupling is at $\phi=4M_{pl}$ and the initial value of the scalar field is at $\phi_i=5.4M_{pl}$. The vast range of potentials outside the coupling still satisfies SR inflation.
• Figure 2: The figure shows the evolution of the scalar field $\phi$ of the local positive coupling form of the Starobinsky potential with respect to the e-foldings number $N$. Around $N\approx45$, the system transitions from SR inflation to USR inflation.
• Figure 3: The figure shows the evolution of the SR parameter $\epsilon_H$ of the local positive coupling form of the Starobinsky potential with the e-foldings number $N$, and at $N\approx45$, $\epsilon_H$ shows a sharp downward trend.
• Figure 4: The figure shows the evolution of the SR parameter $\eta_H$ of the local positive coupling form of the Starobinsky potential with the e-foldings number $N$, where $\eta_H$ temporarily breaks the SR condition at $N\approx45$.
• Figure 5: The relationship between power spectrum with positive coupling form of Starobinsky potential and wave number $k$, where the observation of CMB is satisfied on large scale, but there is a significant improvement in power spectrum on small scale, the color region is excluded by the current observation.