Double inflation as a single origin of primordial black holes for all dark matter and LIGO observations

A primordial black hole (PBH) is one of the leading nonparticle candidates for dark matter (DM). Although several observations severely constrain the amount of PBHs, it was recently pointed out that there is an uncertainty on the microlensing constraints below $\sim {10}^{-10}{M}_{\odot }$, which was ignored originally but may weaken the constraints significantly. In this paper, facing this uncertainty, we investigate the possibility that PBHs can make up all DM in a broad mass spectrum. Moreover, we propose a concrete inflation model that can simultaneously produce PBHs for all DM in a broad mass spectrum around $\mathcal{O}({10}^{-13})M_{\odot }$ and PBHs for LIGO events in a sharp mass spectrum at $\mathcal{O}(10)M_{\odot }$.

Figure 1

The constraints on the parameters of the extended mass function defined by Eq. (14). We use the monochromatic constraints shown in Fig. 2 (including the constraint from the white dwarfs) to derive this result. In each point of ($M_c$, $\sigma$), we calculate the maximum value of $f_{\max }$ under the condition of Eq. (13). The left figure shows the result in the case in which we adopt all the constraints, and the right figure shows the result in the case in which we take into account the uncertainty related to the wave effect and neglect the HSC constraints on $<2\times {10}^{-10}{M}_{\odot }$ PBHs. A green dashed line in the right figure shows the line of $f_{\max }=1$, inside which PBHs can be all the DM.

Figure 2

The PBH mass spectra ($f(M)\equiv \frac{1}{{\mathrm{\Omega }}_{\mathrm{DM}}}\frac{\mathrm{d}{\mathrm{\Omega }}_{\mathrm{PBH}}}{\mathrm{d}\ln M}$) for parameters given in Eqs. (23) (a blue solid line) and (24) (a brown solid line). The red shaded regions show the observational constraints on the monochromatic mass function. The boundaries of the red shade regions correspond to $f_{\mathrm{obs}}(M)$, which are defined in Eq. (12). These constraints come from the observations of the extra-galactic gamma rays from the PBH evaporation ($\mathrm{EG}\gamma$) [62], from the femtolensing events (Femto) [61], from the microlensing events with Subaru HSC (Subaru HSC) [4], with the Kepler satellite (Kepler) [55], with MACHO/EROS/OGLE (MACHO/EROS/OGLE) [52, 53, 54], from the variation of the CMB spectrum (a,b) [63, 64], from the radio and x-ray from accretion (c,d) [65, 66], from the dynamical heating of dwarf galaxies and ultrafaint dwarf galaxies (e,f) [67, 68], and from the distribution of wide binaries (g) [69]. The red dotted line shows the uncertain constraint of the HSC [4] because of the wave effect [56, 57, 58]. The orange shaded regions show the constraint from the existence of white dwarfs in our local galaxy (WD) [51], which is neglected in case 2, and the constraint of the Subaru HSC in $2\times {10}^{-11}{M}_{\odot }<M_{\mathrm{PBH}}<2\times {10}^{-10}{M}_{\odot }$, which is neglected in case 1 (see the text).

Figure 3

The power spectra of the curvature perturbations for parameters given in Eqs. (23) (a blue solid line) and (24) (a brown solid line). Orange shaded regions are excluded by the current constraint on $\mu$ distortion, $|\mu |<9\times {10}^{-5}$ [77], and the effect on the n-p ratio during big bang nucleosynthesis [82]. The black dotted line represents a future constraint by $\mu$ distortion with PIXIE [89], $|\mu |<{10}^{-8}$. For comparison, the power spectrum of the curvature perturbations for $c_{\mathrm{kin}}=0$ and the other parameters given in Eq. (23) is plotted with a purple dashed line (only broad peak).

Figure 4

The induced GW spectra for parameters given in Eqs. (23) (a blue solid line) and (24) (a brown solid line). Green shaded regions are excluded by PTA observations with EPTA [90], PPTA [91], and NANOGrav [92]. Black dotted lines show the prospects of the future experiments: SKA (PTA) [93, 94], eLISA [95], LISA [93, 96], DECIGO [97] (space-based GW interferometer), and the ET [93, 96, 98] (third-generation ground-based GW interferometer). For comparison, the induced GW spectrum for $c_{\mathrm{kin}}=0$ and the other parameters given in Eq. (23) is plotted with a purple dashed line (only broad peak).