Towards closing the window of primordial black holes as dark matter: The case of large clustering

The idea of dark matter in the form of primordial black holes has seen a recent revival triggered by the LIGO detection of gravitational waves from binary black hole mergers. In this context, it has been argued that a large initial clustering of primordial black holes can help alleviate the strong constraints on this scenario. In this work, we show that, on the contrary, with large initial clustering the problem is exacerbated and constraints on primordial black hole dark matter become overwhelmingly strong.

Figure 1

Conversion of PBH energy density (main panel) into gravitational wave radiation [in terms of a corresponding number $\mathrm{\Delta }{N}_{\mathrm{eff}}$ of additional neutrinos (inset)] for $m_0=1M_{\odot }$, $f_{\mathrm{PBH}}=1$, and different theoretical treatments. In grey, we indicate regions excluded by cosmology [35].

Figure 2

GW density parameter per logarithmic frequency interval for $m_0=1M_{\odot }$, $f_{\mathrm{PBH}}=1$, and different theoretical treatments. In grey, we indicate present (solid lower lines) and projected (dashed lower lines) constraints from NANOGrav [48], LISA [49], and LIGO [50] (present O1 and projected design constraint).

Figure 3

Left: Constraints on the allowed fraction $f_{\mathrm{PBH}}$ of PBH DM as a function of the initial PBH mass $m_0$ for large clustering (${\delta }_{\mathrm{dc},0}={10}^6$) in the merger cascade scenario. The thinner black lines indicate contours of the rate-averaged PBH mass $m_{\mathrm{avg}}=(\sum _j{R}_j{m}_j)/\sum _j{R}_j$ at $z=0$. Right: Combined constraints on $f_{\mathrm{PBH}}$ for different clustering parameters ${\delta }_{\mathrm{dc},0}$.

Figure 4

Evolution of mass-integrated merger rate for log-normal mass distributions with $\sigma =1$ and 2 and monochromatic mass distributions considering only one step with $f_{\mathrm{PBH}}=1$, ${\delta }_{\mathrm{dc},0}={10}^6$. Note the additional factor of $a^2$ on the $y$-axis.

Figure 5

Constraints for smaller initial clustering, ${\delta }_{\mathrm{dc},0}={10}^3$ and ${\delta }_{\mathrm{dc},\mathrm{j}}={0.9}^j{\delta }_{\mathrm{dc},0}$. See Fig. 3 for details.