Microlensing events and primordial black holes in the axionlike curvaton model

TL;DR

This work links the Subaru HSC microlensing PBH interpretation to axionlike curvaton scenarios, showing that both Type I and Type II models can enhance small-scale curvature perturbations to produce $M_\text{PBH} \sim 10^{-7}$--$10^{-6}\,M_\odot$ with $f_\text{PBH} \sim \mathcal{O}(0.1)$. The curvature perturbations exhibit non-Gaussianity governed by the curvaton-to-radiation energy ratio at decay, $r_\text{dec}$, which can boost or suppress PBH formation and governs the amplitude of scalar-induced gravitational waves (SIGWs). The paper derives PBH mass functions and SIGW spectra for Type I and II scenarios, showing that SIGWs peak around $f \sim 10^{-5}$ Hz and are within the reach of upcoming detectors like SKA, LISA, and DECIGO; the GW signal’s shape differs between the two types due to distinct curvature spectra and isocurvature dynamics. A Type II variant also yields all-dark-matter PBHs with much smaller masses, while tensions with some microlensing bounds and uncertainties in small-scale perturbations remain important avenues for further study.

Abstract

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.

Figures (5)

• Figure 1: Evolution of $V_\Phi$ and its minimum during inflation. The horizontal axis is the real part of $\Phi$. Upper panel: The potential shape depending on $I$. $V_\Phi$ evolves in the order of red, green, and blue as $I$ decreases. The colored dots denote the potential minima of the potential with the corresponding colors. Lower panel: The trajectory of the potential minimum. The colored dots are the same as in the upper panel. The gray dashed lines denote the approximated relations, $\Phi = \epsilon v^3/(gI^2)$ and $\Phi = \sqrt{v^2/2 - 2gI^2/\lambda}$, which applies for $I \gtrsim \sqrt{\lambda} v/(2 \sqrt{g})$ and $I \lesssim \sqrt{\lambda} v/(2 \sqrt{g})$, respectively.
• Figure 2: Left: Evolution of the energy densities for $r_\mathrm{dec} > 1$. The energy density of the inflaton (blue) remains almost constant during inflation, and becomes matter-like after the end of inflation at $t = t_\mathrm{end}$. Then, the inflaton decays to radiation (light blue) at $t_\mathrm{R}$. The curvaton (red) also remains almost constant in the early stage and starts to oscillate during the MD era dominated by the oscillating inflaton. Then, the oscillating curvaton comes to dominate the universe and decays into radiation (light red) at $t = t_\mathrm{dec}$. Finally, non-relativistic matter (green) dominates the universe for $t > t_\mathrm{eq}$ as in the standard cosmology. Right: The same for $r_\mathrm{dec} < 1$. In this case, the curvaton never dominates the universe, and there is a single RD era.
• Figure 3: Power spectra of the curvature perturbations, $\mathcal{P}_\zeta$. The blue, red, and violet lines represent the results for the type II model with the parameter sets in Table \ref{['tab: type II parameter']}. The curvature perturbations have peaks due to the evolution of $\varphi_0$ during inflation. Due to the effective mass of $\delta \sigma$ in the early stage of inflation, they are suppressed for small $k$. We do not show the short modes that reenter the horizon before the curvaton decay. While the red and blue lines lead to the production of PBHs explaining the microlensing events, the violet line corresponds to PBHs with smaller masses. The green line represents the result for the type I model.
• Figure 4: PBH fraction to dark matter, $f_\mathrm{PBH}$, for the type II model with the parameter sets in Table \ref{['tab: type II parameter']} (blue, red, and violet) and the type I model with the parameter set in Eq. \ref{['eq: type I parameters']} (green). The blue- and red-shaded regions represent the PBH interpretation of the 12 candidates and 4 secure candidates for microlensing events observed in Subaru HSC observations Sugiyama:2026kpv, respectively. The green-shaded region represents the estimate by Ref. Niikura:2019kqi interpreting the ultrashort-timescale microlensing events in the 5-year OGLE data Mroz:2017mvf as originating from PBHs. The gray-shaded regions represent the observational upper bounds on the PBH abundance by EROS EROS-2:2006ryy, HSC Croon:2020ouk, OGLE-III+OGLE-IV Mroz:2024mse, the high-cadence survey by OGLE-IV Mroz:2024wia, X-ray background Tan:2024nbx, and the 21 cm measurement Mittal:2021egv. The last two limits are due to the evaporation of PBHs and are taken from PBHbounds PBHbounds.
• Figure 5: Power spectra of the gravitational waves in the type II (blue, red, and violet) and type I (green) axionlike curvaton models. The colors are the same as in Figs. \ref{['fig: Pzeta']} and \ref{['fig: fPBH']}. The gray lines represent the future sensitivities of the Square Kilometre Array (SKA) Janssen:2014dkaWeltman:2018zrl, THEIA Garcia-Bellido:2021zgu, $\mu$Ares Sesana:2019vho, Laser Interferometer Space Antenna (LISA) LISA:2017pwj, and DeciHertz Interferometer Gravitational-Wave Observatory (DECIGO) Kawamura:2006up. The sensitivities of SKA, LISA, and DECIGO are taken from Ref. Schmitz:2020syl. The gray violins on the nHz scale represent the result of the NANOGrav 15 yr data set NANOGrav:2023gor.