Constraints on the Primordial Black Hole Abundance using Pulsar Parameter Drifts

Primordial black holes (PBHs) provide a compelling interpretation for the binary black holes (BBHs) observed by ground-based gravitational-wave (GW) detectors, especially for those BBHs in the theoretical mass gap. In the early Universe, the scalar perturbations required to produce such PBHs inevitably generate scalar-induced GWs (SIGWs). These SIGWs peak in the sub-nanohertz band, and manifest secularly as measurable jerk-like drifts in the second derivative of pulsar spin periods. In this Letter, we perform the first search for SIGWs using pulsar parameter drifts, and place a 95% confidence-level upper limit on the PBH abundance of $f_{\mathrm{P}\mathrm{B}\mathrm{H}}<{10}^{-10}$ over the mass range $[3\times {10}^{-1},4\times {10}^4]M_{\odot }$. Our results strongly disfavor a PBH origin for the BBHs currently detected by the LIGO-Virgo-KAGRA (LVK) Collaborations.