Primordial black hole constraints for curvaton models with predicted large non-Gaussianity

TL;DR

This work demonstrates that primordial black hole (PBH) constraints on small-scale curvature perturbations are highly sensitive to the non-Gaussian shape of those perturbations, particularly in curvaton scenarios where $\zeta$ has a χ^2-type form. By deriving the PDF for non-Gaussian curvature perturbations, applying a Gaussian smoothing, and computing PBH mass spectra via the Press-Schechter formalism, the authors show that PBH limits on the curvature power spectrum $\mathcal{P}_\zeta$ can differ by orders of magnitude from Gaussian expectations, with $\mathcal{P}_\zeta^0$ constrained to roughly $10^{-4}$ to $10^{-2.5}$ depending on the spectral index $n$ and formation threshold $\zeta_c$. The analysis connects PBH abundances to curvaton parameters, such as $\Omega_\sigma$, and indicates that PBHs can outpace single-field inflation bounds in constraining small-scale perturbations. Overall, the paper highlights PBHs as a powerful probe of early-universe physics and non-Gaussianity in multi-field inflation scenarios, and outlines pathways to tighten constraints for specific parameter choices.

Abstract

We consider the early Universe scenario which allows for production of non-Gaussian curvature perturbations at small scales. We study the peculiarities of a formation of primordial black holes (PBHs) connected with the non-Gaussianity. In particular, we show that PBH constraints on the values of curvature perturbation power spectrum amplitude are strongly dependent on the shape of perturbations and can significantly (by two orders of magnitude) deviate from the usual Gaussian limit ${\cal P}_ζ\lesssim 10^{-2}$. We give examples of PBH mass spectra calculations and PBH constraints for the particular case of the curvaton model.

Figures (4)

• Figure 1: The form of the distribution (\ref{['pzeta-curvaton']}) for $\sigma_\zeta^2 = 2\times 10^{-4}$. Dashed lines show the considered values of $\zeta_c$ ($0.75$ and $1$, see text).
• Figure 2: A sketch that illustrates a relation between curvaton-generated and inflaton-generated curvature perturbation power spectra for the scenario of PBH production that we consider.
• Figure 3: Examples of PBH mass spectra calculated for the curvaton model, for several sets of parameters $n$ and $\zeta_c$. For all curves, ${\@fontswitch{}{\mathcal{}} P}_\zeta ^0 = 4\times 10^{-4}$. The mass $M_{BH}^{min}=f_h M_h(t_e)$ and $t_e$ is the moment of time when perturbation with comoving wave number $k_e$ enters horizon.
• Figure 4: The limits on the maximum value of curvature perturbation power spectrum ${\@fontswitch{}{\mathcal{}} P}_\zeta^0$ from PBH non-observation, for the curvaton model, for several sets of parameters $n$ and $\zeta_c$. The forbidden regions are above of the corresponding curves. $M_h$ is the horizon mass at the moment of time when the perturbation with comoving wave number $k_e$ enters horizon. The spectrum is parameterized as (\ref{['Pzeta-curvaton-par']}).