Search for the Stochastic Gravitational-wave Background Induced by Primordial Curvature Perturbations in LIGO’s Second Observing Run

Primordial density perturbations generate a stochastic background of gravitational waves (GWs) through non-linear mode couplings upon their horizon reentry. In this Letter, we report on a search for such a stochastic GW background in the data of the two LIGO detectors during their second observing run (O2). We focus on the primordial perturbations in the range of comoving wavenumbers $10^{16}-10^{18}~{\rm Mpc}^{-1}$ for which the stochastic background falls within the detectors' sensitivity band. We do not find any conclusive evidence of this stochastic signal in the data, and thus place the very first GW-based constraints on the amplitude of the power spectrum at these scales. We assume a lognormal shape for the power spectrum and Gaussian statistics for the primordial perturbations, and vary the width of the power spectrum to cover both narrow and broad spectra. Derived upper limits ($95\%$) on the amplitude of the power spectrum are $0.01-0.1$. As a byproduct, we are able to infer upper limits on the fraction of the Universe's mass in ultralight primordial black holes ($M_\mathrm{PBH} \simeq 10^{-20}-10^{-19}M_{\odot}$) at their formation time to be $\lesssim 10^{-25}$. If Hawking evaporation is discarded, this can be translated to constraints on the fraction of dark matter today in the form of such ultralight primordial black holes, which can be as stringent as $\sim 10^{-15} - 10^{-5}$.