http://arxiv.org/abs/2210.03476
Scalar perturbations in the early Universe create over-dense regions that can collapse into primordial black holes (PBH). This process emits scalar-induced gravitational waves (SIGW) that behaves like an extra radiation component and contributes to the relativistic degrees of freedom ($N_{\rm{eff}}$). We show that $N_{\rm{eff}}$ limits from cosmic microwave background (CMB) give promising sensitivities on both the abundance of PBHs and the primordial curvature perturbation ($\mathcal{P}{\mathcal{R}}(k)$) at small scales. We show that {\it Planck} and ACTPol data can exclude supermassive PBHs with peak mass $M{\bullet} \in [3 \times 10^{5}, 5 \times 10^{10}] {\rm{M}}{\odot}$ as the major component of dark matter, depending on the shape of the PBHs mass distribution. Future CMB-S4 mission is capable of broadening this limit to a vast PBH mass window of $M{\bullet} \in [8 \times 10^{-5}, 5 \times 10^{10}] {\rm{M}}{\odot}$, covering sub-stellar masses. These limits correspond to the enhanced sensitivity of $\mathcal{P}{\mathcal{R}}(k)$ on scales of $k \in [10^1, 10^{22}]\ \rm{Mpc^{-1}}$, which is much smaller than those scales probed by direct perturbation power spectra (CMB and large-scale structure).
J. Cang, Y. Ma and Y. Gao
Mon, 10 Oct 22
19/59
Comments: 7 pages, 3 figures