Implications for primordial black holes from cosmological constraints on scalar-induced gravitational wave

TL;DR

This paper uses cosmological constraints on extra radiation from scalar-induced gravitational waves to set limits on primordial black holes and small-scale curvature perturbations, excluding certain PBH mass ranges as dark matter candidates.

Contribution

It introduces a novel method to constrain primordial black holes using $N_{ m{eff}}$ measurements from cosmological data, linking gravitational wave emissions to PBH formation scenarios.

Findings

Excludes supermassive PBHs as dominant dark matter for certain mass ranges.

Future CMB observations can extend constraints to smaller PBH masses.

Tightens bounds on small-scale curvature perturbations across a wide range of scales.

Abstract

Sufficiently large scalar perturbations in the early Universe can create over-dense regions that collapse into primordial black holes (PBH). This process is accompanied by the emission of scalar-induced gravitational waves (SIGW) that behave like an extra radiation component, thus contributing to the relativistic degrees of freedom ($N_{\rm{eff}}$). We show that the cosmological constraints on $N_{\rm{eff}}$ can be used to pose stringent limits on PBHs created from this particular scenario as well as the relevant small-scale curvature perturbation ($\mathcal{P}_{\mathcal{R}}(k)$). We show that the combination of cosmic microwave background (CMB), baryon acoustic oscillation (BAO) and Big-Bang nucleosynthesis (BBN) datasets can exclude supermassive PBHs with peak mass $M_{\bullet} \in [5 \times 10^{5}, 5 \times 10^{10}]\,{\rm M}_{\odot}$ as the major component of dark matter, while the detailed constraints depend on the shape of the PBHs mass distribution. The future CMB mission like CMB-S4 can broaden this constraint window to a much larger range $M_{\bullet} \in [8 \times 10^{-5}, 5 \times 10^{10}]\,{\rm M}_{\odot}$, covering sub-stellar masses. These limits on PBH correspond to a tightened constraint on $\mathcal{P}_{\mathcal{R}}$ on scales of $k \in [10, 10^{22}]\ {\rm{Mpc^{-1}}}$, much smaller than those probed by direct CMB and large-scale structure power spectra.