Critical collapse and black hole formation within an expanding perfect fluid

Following on after three previous papers discussing the formation of primordial black holes in the early universe during the radiation dominated era, we present here related results considering the theoretical possibility of having a fluid with a different sound speed. In practice we vary the parameter w of the equation of state p = we between 0 and 1, where e is the energy density, and p the pressure of the fluid. We consider also the possibility of having a cosmological constant interpreted as a vacuum energy component (corresponding to w = -1) revising the results presented in our first paper of this series, having now a more refined numerical code available. To perform our simulations we have fine tuned our previous computer code allowing us to observe that the nature of the critical collapse is conserved for all the different values of w considered, in agreement with previous studies of ideal collapses done in a different context from PBHs. As already done in our previous works, we start the simulations with initial supra-horizon scale perturbations of a type which could have come from inflation, characterized by a pure growing mode component.