Sufficiently large scalar perturbations in the early universe can create overdense regions that collapse into primordial black holes (PBHs). This process is accompanied by the emission of scalar-induced gravitational waves that behave like an extra radiation component, thus contributing to the relativistic degrees of freedom (N eff). We show that the cosmological constraints on N eff can be used to pose stringent limits on PBHs created from this particular scenario as well as the relevant small-scale curvature perturbation (). We show that the combination of cosmic microwave background (CMB), baryon acoustic oscillation, and Big Bang nucleosynthesis data sets can exclude supermassive PBHs with peak mass M • ∈ [5 × 105, 5 × 1010] M ⊙ as the major component of dark matter, while the detailed constraints depend on the shape of the PBHs’ mass distribution. A future CMB mission such as CMB-S4 can greatly broaden this constraint window to M • ∈ [8 × 10−5, 5 × 1010] M ⊙, covering substellar masses. These limits on PBHs correspond to a tightened constraint on on scales of k ∈ [10, 1022] Mpc−1, much smaller than those probed by direct CMB and large-scale structure power spectra.
Read full abstract