Thermodynamic constraint on primordial black hole formation in the radiation dominated epoch

It has been suggested that the overdense region as a result of inhomogeneities in the early Universe would have undergone a collapse into the primordial black holes(PBH). In this work, we discuss a possible constraint on the PBH formation in the radiation dominated epoch by imposing the generalized second law of thermodynamics in the context of spherically collapsing scenario. It is found that both the critical temperature $T_c$ over which the formation of PBH is not possible and the lower bound on the mass of PBH depend on the number of degrees of freedom at the time of PBH formation. In the standard model, one can show that the lower bound on the mass of PBH known in the literature, of order Planck mass, is consistent with the thermodynamic constraint constructed in this work. We also pointed out the possibility that the critical temperature(lower bound on PBH mass) can be lowered(increased) provided the number of relativistic degrees of freedom of the Universe is increasing substantially beyond the standard model.