Primordial black hole formation from an axion-like curvaton model

TL;DR

The paper addresses whether PBHs can account for CDM and seed SMBHs by employing an axion-like curvaton that generates a highly blue-tilted curvature-perturbation spectrum at small scales, while the inflaton sets the large-scale spectrum. The authors develop a SUSY-based curvaton model, derive the curvaton-induced $P_{ζ,curv}(k)$ with a blue tilt $n_σ \sim 2$–$4$, and compute PBH formation and abundance from the resulting density perturbations. They show that PBHs with masses in the range $M_{BH} \sim 10^{17}-10^{27}$ g can dominate CDM in certain parameter regions, and that much heavier PBHs around $10^5 M_⊙$ can serve as seeds for SMBHs, yielding a narrow mass spectrum when invoked for SMBH seeding. The analysis yields constraints on $H_{inf}$, $f$, $m_σ$, $Λ$, and the reheating temperature, and demonstrates that the scenario can be realized within and beyond SUSY, offering a testable alternative to WIMP dark matter and a mechanism for SMBH formation.

Abstract

We argue that the existence of the cold dark matter is explained by primordial black holes.We show that a significant number of primordial black holes can be formed in an axion-like curvaton model, in which the highly blue-tilted power spectrum of primordial curvature perturbations is achieved.It is found that the produced black holes with masses $\sim 10^{20} -10^{38} \mathrm{g}$ account for the present cold dark matter.We also argue the possibility of forming the primordial black holes with mass $\sim 10^5 M_{\odot}$ as seeds of the supermassive black holes.

Figures (6)

• Figure 1: The ratio of the smoothed variance of density perturbation to the power spectrum of curvature perturbation are shown. The horizontal axis is the wave number corresponding to the smoothing scale as $k=R^{-1}$ divided by $k_*$. This curve is independent of $n_\sigma$.
• Figure 2: The energy density fraction of the PBH at the formation is shown. The horizontal axis correspond to $\mathcal{P}_{\zeta,\mathrm{curv}}$ in Fig. \ref{['Fig2a']} and $H_\mathrm{inf} / f \theta$ in Fig. \ref{['Fig2b']}. In Fig. \ref{['Fig2a']}, the solid red line and the dashed green line correspond to $\alpha = 1$ and $\alpha = 0.1$ respectively. In Fig. \ref{['Fig2b']}, the thick (thin) solid red line corresponds to $r = 1$ and $\alpha=1~(0.1)$ and the thick dashed green line corresponds to $r=0.1$ and $\alpha = 1$. Breaking point of each line in Fig. \ref{['Fig2b']} corresponds to $\delta \sigma / \sigma = 1$. The dotted blue line (the small-dotted magenta line) corresponds to the upper limit in the case of $M_\mathrm{BH} = 10^{27}~(10^{17})~\mathrm{g}$, which comes from the current observational value of the CDM density parameter : $\Omega_\mathrm{CDM} = 0.23$.
• Figure 3: The mass spectrum of PBH, $dn_\mathrm{PBH}/dM_\mathrm{BH}$, is shown. The solid red line and dashed green line corresponds to $M_\mathrm{min}/M_* = 10^{-8}$ and $M_\mathrm{min}/M_* = 10^{-3}$ respectively and they are normalized by the their own peak values. They are independent of $n_\sigma$.
• Figure 4: The allowed parameter region in which PBHs become the dominant component of the CDM in our model is shown. The allowed region is inside the respective contours. The dotted-blue line and the solid-red line correspond to the boundary in the case of $n_\sigma =$ 3 and 2 respectively. The dashed-and-dotted-cyan line is the lower limit on the PBH mass coming from the upper limit on the tensor-to-scalar ratio. We have taken $r=1$ and $\theta = 1$.
• Figure 5: The allowed regions for the PBH to be the dominant dark matter in $f$ -- $m_\sigma$ plane and $f$ -- $\Lambda$ plane are shown. Inside the thick solid-red (dashed-green) lines, the conditions (\ref{['f-m_sigma']}) and (\ref{['f-m_sigma2']}) are satisfied for $\kappa = 1~(0.01)$. The thick (thin) dashed-and-dotted-cyan lines corresponds to the upper limit which comes from the maximum mass of PBH dark matter: $M_{\rm BH} = 10^{27}~{\rm g}$ for $\kappa = 1~(0.01)$, so the allowed parameters are inside the yellow shaded regions. The thin small-dotted magenta lines correspond to $M_{\rm BH} = 10^{25}~{\rm g}$ for $\kappa = 0.01$. We have taken $n_\sigma = 2$ and $\theta = 1$ and assumed $m_\sigma > \Gamma_I$ in both figures.