Constraint on the abundance of primordial black holes in dark matter from Planck data

TL;DR

The paper addresses whether primordial black holes can constitute a significant fraction of dark matter by analyzing Planck 2015 CMB data within two reionization histories. It models PBH-induced ionization via $x_{e,\text{pbh}}(z)$ and constrains the resulting optical depth contribution $\Delta\tau_e$ using CAMB/CosmoMC with Planck TT,TE,EE+lowP+lensing data, finding tight upper limits on PBH abundance that improve previous WMAP constraints by about two orders of magnitude. These bounds translate into merger-rate limits for PBH binaries, yielding $ER(t_0)<0.002$ Gpc$^{-3}$ yr$^{-1}$ at $M_{\text{pbh}}=30 M_\odot$, with higher rates for smaller masses, thereby making GW150914 unlikely to be PBH-origin. The study highlights how large-scale CMB polarization can serve as a powerful probe of PBHs in the early universe and informs expectations for future gravitational-wave observations of PBH binaries.

Abstract

We use Planck data released in 2015 to constrain the abundance of primordial black holes (PBHs) in dark matter in two different reionization models (one is the instantaneous reionization and the other is the asymmetric reionization), and significantly improve the upper limits on the abundance of PBHs from WMAP 3-year data by around two orders of magnitude. Furthermore, these new limits imply that the event rates of mergers of PBH binaries (Gpc$^{-3}$ yr$^{-1}$) are less than $0.002$ for $M_\text{pbh}=30M_\odot$, $5$ for $M_\text{pbh}=10M_\odot$ and $2000$ for $M_\text{pbh}=2M_\odot$ at $95\%$ confidence level (C.L.), and thus GW150914 seems very unlikely produced by the merger of a PBH binary.

Figures (5)

• Figure 1: CMB angular power spectra. Here the total optical depth $\tau_e=0.134$ is kept fixed and the tensor-to-scalar ratio is $r=0.1$. The solid curves and dashed curves correspond to $x_{e0}=0$ (without PBHs) and $x_{e0}=1\times 10^{-3}$ respectively.
• Figure 2: The likelihood of $\Delta\tau_e$ in the instantaneous and asymmetric reionzation models.
• Figure 3: The evolution of ionization fraction $x_e(z)$ for different reionization models. The black solid curve corresponds to the instantaneous reionization model without PBHs, and the red dotted and blue dashed curves illustrate the $95\%$ limits for the instantaneous and asymmetric reionization models with PBHs, respectively.
• Figure 4: The upper limit on the abundance of PBHs in dark matter at $95\%$ confidence level. Here the black solid line represents our results and the grey dashed line corresponds to the constraints from WMAP 3-year data.
• Figure 5: The upper limit on the event rate of mergers of PBH binaries. The dashed and solid black lines illustrate the limits at $68\%$ and $95\%$ confidence level respectively.