2026/07/30 by Albert Escrivà
Physics and Astronomy · #astro-ph.CO #gr-qc #hep-ph #hep-th
72 pages and 24 figures. v2: additional numerical results included, references added, and typos corrected
arxiv created 2026/07/30 · arxiv updated 2026/07/31
In the standard curvature-perturbation scenario, PBHs form from the collapse of superhorizon curvature fluctuations after horizon re-entry. The predicted abundance is exponentially sensitive to the collapse threshold and hence to the shape of the primordial curvature profile. In this work we develop a finite-action framework to describe curvature-profile dispersion around representative peak profiles. Using a multipolar Fourier-Bessel decomposition, we separate the local peak variables of the Gaussian field from residual radial and angular deformations, normalized by their Gaussian action. We apply the formalism to spherical numerical-collapse examples in order to isolate the effect of radial shape dispersion. For finite-width spectra, and in the presence of logarithmic local non-Gaussianity, we compute the collapse threshold as a function of a coherent shape variable and combine the result with peak statistics. We find that the dominant contribution to the PBH abundance is not necessarily the conditional-mean reference profile, nor simply the profile with the lowest threshold. Instead, it is selected by a competition between the Gaussian cost of realizing a coherent deformation and the exponential gain associated with lowering the collapse threshold. Broad spectra and negative non-Gaussianity can make rare shape deformations dominate the abundance. In the examples studied here, the dominant branches can correspond to several-sigma coherent shape fluctuations while enhancing the integrated abundance by orders of magnitude. Equivalently, including shape dispersion can reduce the power-spectrum amplitude required to obtain a fixed PBH abundance. Our results show that residual profile dispersion is a genuine statistical ingredient in PBH formation and can be quantitatively important for accurate abundance estimates.