Constraints on primordial black holes with CMB spectral distortions

In the mixed dark matter scenarios consisting of primordial black holes (PBHs) and weakly interacting massive particles (WIMPs), WIMPs can be accreted onto PBHs to form ultracompact minihalos (UCMHs) with a density spike in the early universe. Compared with the classical dark matter halo, UCMHs are formed earlier and have a higher density of center. Since the annihilation rate is proportional to the squared number density of WIMPs, it is expected that WIMPs annihilation within UCMHs is enhanced and has influences on the early universe. Between the time of recombination and matter-radiation equality, the energy released from WIMPs annihilation within UCMHs is injected into the Universe resulting in cosmic microwave background $y$-type distortion. We investigate these effects and derive the upper limits on the abundance of PBHs taking advantage of the observational results of a far infrared absolute spectrophotometer (FIRAS). We find that for the WIMPs mass range $1\le m_{\chi }\le 1000\mathrm{GeV}$, the upper limits on the abundance of PBHs are $5\times {10}^{-3}\le {\mathrm{\Omega }}_{\mathrm{PBH}}\le 5\times {10}^{-2}$.

Figure 1

Upper limits on the abundance of PBHs, ${\mathrm{\Omega }}_{\mathrm{PBH}}={\rho }_{\mathrm{PBH}}/{\rho }_{c,0}$, by requiring $y_{\mathrm{DM}}<1.5\times {10}^{-5}$. Here we have set the thermally averaged annihilation cross section $⟨\sigma v⟩=3\times {10}^{-26}\mathrm{c}{\mathrm{m}}^3{\mathrm{s}}^{-1}$.

Figure 2

Comparison with a few other constraints on the fraction of DM in PBHs, $f_{\mathrm{PBH}}={\mathrm{\Omega }}_{\mathrm{PBH}}/{\mathrm{\Omega }}_{\mathrm{DM}}$. The horizontal dashed lines show the upper limits obtained by us for the DM mass $m_{\chi }=1$, 10, 100 and 1000 GeV. Other constraints are from: (1) the merger rate of PBHs in light of the sensitivity of LIGO (labeled “LIGO”) [56]; (2) the influence of PBHs on the dynamical evolution of stars in the dwarf galaxy Segue I (labeled “Segue I”) [57]; (3) investigating the influence of accreting PBHs on the CMB with Planck data (labeled “Planck”) [58]; (4) the gravitational lensing effects based on EROS (labeled “EROS”) [55]; (5) the contribution of DM annihilation within UCMHs to the EGB (labeled “EGB”) [30]; and (6) the influence of DM annihilation within UCMHs on the CMB (labeled “CMB”) [25].