Primordial Black Hole from Tensor-induced Density Fluctuation: First-order Phase Transitions and Domain Walls

Abstract

Gravitational waves generated by violent processes in the early Universe necessarily couple to scalar perturbations beyond linear order. We show that tensor perturbations produced by first-order phase transitions and by annihilating domain-wall networks source density fluctuations at second order, thereby opening a distinct channel for primordial-black-hole (PBH) formation. We compute the tensor-induced density spectrum for both sources and map the resulting PBH abundance onto the macroscopic parameters $(\hat{I}\pm ,{\hat{I}}^2/H,T_{\star })$ of a first-order phase transition and $(\hat{I}{\pm }_{\mathrm{ann}},V_{\mathrm{bias}},\ddot{I}ƒ)$ of a domain-wall network. Existing PBH limits therefore impose complementary constraints on early-Universe sources of stochastic gravitational waves. We find viable regions where one can have an observable gravitational-wave background and an appreciable abundance of asteroid-mass PBHs, including benchmark points that saturate the dark-matter abundance. Our results establish a direct, testable correlation among the source scale, the gravitational-wave spectrum, and the PBH mass function, distinguishing this tensor-induced channel from PBHs formed through delayed vacuum decay or direct defect collapse. We also discuss viable particle physics origin of such FOPT and DW, and therefore, constraints on such microphysics, either in the visible, or in dark sector models.

6 pages, 24 pages SM, updated discussion on causality, perturbativity, and connection to particle physics models