Primordial black holes (PBHs) are potential candidates for dark matter and offer a unique way to probe the inflationary models that describe the very early universe. They are hypothesized to have formed from the gravitational collapse of regions with extremely high density in the moments after the Big Bang. As a result, the predicted number of PBHs provides a way to test the properties of the small density fluctuations generated during inflation, a brief period of extremely rapid expansion that occurred fractions of a second after the Big Bang.

In most conventional calculations, the production rate of PBHs is estimated by assuming that cosmological perturbations follow a nearly Gaussian distribution. Black holes are then assumed to form wherever the amplitude of a perturbation exceeds a certain threshold value. However, the curvature threshold is sensitive to surrounding environmental effects that are not directly related to the local collapse dynamics, introducing ambiguity in the predicted abundance. Moreover, the density perturbation has an upper bound at horizon entry, which causes its distribution near the collapse threshold to deviate from a simple Gaussian description.

To address the inherent limitations of earlier Press–Schechter–based methods, we construct a new framework based on peak theory for estimating the primordial black hole mass function and abundance. This framework eliminates the dependence on arbitrary window functions, replaces the environmentally sensitive curvature threshold with a local and physically meaningful compaction function as the formation criterion, and consistently incorporates the relevant nonlinear general relativistic effects.

The compaction function is defined as the mass excess above the background divided by the area radius. For nearly spherical perturbations, it is equivalent to half of the volume-averaged density perturbation at the moment of horizon entry. PBH formation is assumed to occur when the maximum value of this function exceeds a specified threshold.

Our results offer a significant revision to previous estimates. We find that the predicted mass of PBHs is shifted to larger scales by about an order of magnitude compared to conventional calculations. Furthermore, the overall abundance of PBHs increases significantly. By refining the theoretical calculation of the PBH mass function and removing the approximations and model dependence inherent in earlier methods, this approach deepens our understanding of PBH formation and the statistics of the early Universe, earning the Outstanding Paper Award of the Physical Society of Japan in 2026.

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