Critical collapse and black hole formation within an expanding perfect fluid

Abstract. Following on after three previous papers discussing the formation of primordial black holes during the radiation-dominated era of the early universe, we present here results for a related toy problem where the parameter w in the equation of state is allowed to take values different from 1/3. This can give useful insight into the main case of interest. 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 the first paper of this series with use of the present more-refined version of our numerical code. As in our previous work, we have started our simulations with initial supra-horizon scale perturbations of a type which could have come from inflation, characterized by a pure growing-mode component. We have verified that the critical collapse behaviour is preserved in this context for all of the different values of w considered, matching well with the parameter values found for the scaling laws in more idealized circumstances