Microlensing events and primordial black holes in the axionlike curvaton model

Recently, Subaru Hyper Suprime-Cam (HSC) observations found 12 candidates for microlensing events. These events can be explained by primordial black holes (PBHs) with masses of $10^{-7}$-$10^{-6} M_\odot$ and a fraction of all dark matter of $f_\mathrm{PBH} = \mathcal{O}(10^{-1})$. In this paper, we consider the PBH production in two types of the axionlike curvaton models, which predict an enhancement of the curvature perturbations on small scales. We show that the microlensing events can be explained in the axionlike curvaton model and discuss the cosmological implications such as gravitational waves.

💡 Research Summary

The paper addresses the recent Subaru Hyper Suprime‑Cam (HSC) detection of twelve microlensing candidates—four of which are deemed secure—and interprets them as signatures of primordial black holes (PBHs) with masses in the range $10^{-7}$–$10^{-6},M_\odot$ that constitute a fraction $f_{\rm PBH}=O(10^{-1})$ of the total dark matter. To generate PBHs in this narrow mass window, the authors explore two variants of the axion‑like curvaton scenario (type I and type II), both of which can produce a pronounced enhancement of the curvature perturbation power spectrum on the relevant small scales.

In the type II model a complex scalar field $\Phi$ has its radial component stabilized near the origin during early inflation, then rolls down a potential at a critical time $t_{\rm peak}$, causing the phase field $\sigma$ (the curvaton) to acquire a scale‑dependent effective mass. This leads to a power spectrum $P_{\delta\sigma}(k)$ that is blue‑tilted for $k<k_{\rm peak}$, red‑tilted for $k>k_{\rm peak}$, and peaks sharply at $k_{\rm peak}$. The type I model instead features a radial component that starts from a large field value and rolls down monotonically, yielding a broadly blue‑tilted spectrum without a distinct peak.

A central role is played by two parameters: the curvaton‑to‑radiation energy ratio at curvaton decay, $r_{\rm dec}\equiv\rho_\sigma/\rho_I$, and the local‑type non‑Gaussianity parameter $f_{\rm NL}$. When $r_{\rm dec}\gg1$, the curvaton dominates the energy density and $f_{\rm NL}<0$, suppressing PBH formation. Conversely, $r_{\rm dec}\lesssim1$ gives $f_{\rm NL}>0$, which enhances the high‑density tail of the perturbation distribution and thus boosts PBH production.

The curvature perturbation after curvaton decay is
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