Primordial black hole formation for an anisotropic perfect fluid: Initial conditions and estimation of the threshold

Abstract: This work investigates the formation of primordial black holes within a radiation fluid with an anisotropic pressure. We focus our attention on the initial conditions describing cosmological perturbations in the super horizon regime, using a covariant form of the equation of state in terms of pressure and energy density gradients. The effect of the anisotropy is to modify the initial shape of the cosmological perturbations with respect to the isotropic case. Using the dependence of the threshold $\delta_\mathrm{c}$ for primordial black holes with respect to the shape of cosmological perturbations, we estimate here how the threshold is varying with respect to the amplitude of the anisotropy. If this variation is large enough it could lead to a significant variation of the abundance of PBHs.