Primordial black hole formation in bulk-viscous cosmology

We investigate primordial black hole (PBH) formation in a cosmological background with bulk viscosity. Using numerical simulations, we determine the collapse threshold and the resulting PBH mass. We find that the critical threshold $\mu_c$ retains a dependence on the equation-of-state parameter $w$ similar to that in the inviscid case, but is enhanced by an amount comparable to the bulk-viscosity strength $\epsilon$. For fixed $w$, the increase in $\mu_c$ is approximately linear in $\epsilon$. By fitting the standard critical-scaling law for near-threshold collapse, we find that the bulk viscosity leads to an enhancement in the resulting PBH mass. These results indicate that bulk viscosity can systematically modify both the PBH threshold and PBH mass scaling law in the early universe.