Threshold of primordial black hole formation against velocity dispersion in matter-dominated era

Abstract We study the effects of velocity dispersion on formation primordial black holes (PBHs) in a matter-dominated era. The is generated through nonlinear growth perturbations and has potential to impede gravitational collapse thereby PBHs. To make discussions clear, we consider two distinct length scales. larger one where occurs which could lead PBH formation, smaller develops due interactions. estimate effect by comparing free-fall timescale for particle cross collapsing region. As demonstration, log-normal power spectrum initial density perturbation with peak value σ 0 2 at scale that corresponds scale. find threshold δ̃ th horizon entry scales as ∝ 2/5 ≪ 1.