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We study the properties of the stochastic gravitational wave background(SGWB) resulting from the mergers of primordial black holes (PBH) that formedfrom the collapse of sub-horizon regions in the early universe. We adopt amodel-independent approach, where we parameterize the fraction $f_H$ of thewavelength of the perturbation mode in units of the horizon radius when thepatch starts to gravitationally collapse. Assuming a monochromatic spectrum ofisocurvature perturbations and spherically-symmetric density perturbations, weinvestigate the isotropic SGWB energy density and angular power spectrum atvarious frequencies, PBH masses, and horizon size fractions. The key effect ofsub-horizon formation is a change in the PBH mass function and formationredshift, which, in turn, affects gravitational wave (GW) observables. We findthat sub-horizon PBH formation in general enhances the isotropic SGWB energydensity and the absolute angular power spectrum. However, the quasi-monotonicincreases in both quantities as $f_H$ decreases cease when the chirp mass ofthe binary PBHs reaches a mass threshold determined by the frequency ofobservation; the isotropic SGWB energy density spectrum significantly dropsabove the corresponding cutoff frequency.

On the Anisotropy of the Stochastic Gravitational Wave Background from Sub-Horizon-Collapsed Primordial Black Hole Mergers