Owais Farooq | Searcharxiv

arXiv2026

Primordial Black Holes (PBHs) and The Signatures of Cosmic Non-Gaussianity

Primordial black-hole formation depends exponentially on the far tail of the primordial curvature-perturbation distribution. That sensitivity makes the small-scale collapse problem a sharp probe of primordial non-Gaussianity. We study the curvaton scenario by deriving the curvature perturbation from the exact sudden-decay relation, obtaining the full probability density function through an explicit branchwise change of variables from the Gaussian curvaton-field fluctuation, and evaluating the primordial black-hole formation fraction from the exact non-perturbative tail. The derivation is written step by step, with the support of the distribution, the Jacobian, the normalization, and the small-fluctuation expansion displayed in analytic form. We place the exact curvaton prediction beside the Gaussian benchmark and beside an exact local quadratic benchmark in which the non-Gaussian probability density is also computed without an Edgeworth truncation. We then replace the scale-by-scale variance-matching ansatz by a self-consistent curvaton fluctuation model in which the dimensionless field fluctuation spectrum is specified once, the smoothed curvaton variance is computed directly, the exact collapse fraction follows with no further fitting on each scale, and the induced gravitational-wave background is generated from the linear curvaton two-point spectrum implied by the same model. The resulting mass functions are confronted with a conservative current constraint envelope motivated by recent primordial-black-hole reviews, and the induced gravitational-wave spectra are displayed against the PTA, LISA, and DECIGO sensitivity windows. The final figures are generated from a single mathematically consistent numerical pipeline.

astro-ph.CO↗

arXiv2026

Press-Schechter Formalism and The PBH Mass Distributions

Primordial black holes (PBHs) can form during radiation domination from rare primordial perturbations that re-enter the Hubble radius and undergo gravitational collapse. We derive PBH mass distributions using Press--Schechter theory completed by the excursion-set first-crossing construction. We define the smoothed density contrast $δ_R$ and its variance $S(R)=σ^2(R)$, and connect $S$ to the primordial curvature spectrum $\mathcal{P}_{\mathcal R}(k)$ through the radiation-era transfer. For Gaussian statistics and a constant collapse threshold $δ_c$, the formation fraction is an $\operatorname{erfc}$ tail with a controlled rare-event asymptotic. For a sharp-$k$ filter, $δ(S)$ is Markovian; solving the diffusion equation with an absorbing barrier yields the first-crossing density $f(S)=\frac{δ_c}{\sqrt{2π}}S^{-3/2}\exp\!\big(-δ_c^2/(2S)\big)$. This gives a differential formation fraction $\mathrm{d}β/\mathrm{d}\ln M=f(S)\,\big|\mathrm{d}S/\mathrm{d}\ln M\big|$ and a mass-conserving formation-era mass function $\mathrm{d}n_{\mathrm{PBH}}/\mathrm{d}M$. We then map to the present-day PBH dark-matter fraction per logarithmic mass, $f_{\mathrm{PBH}}(M)$, using horizon-entry scaling $M\propto k^{-2}$ and radiation-era redshifting.

astro-ph.CO↗