Cosmic evolution and primordial black hole evaporation

Abstract

A cosmological model in which primordial black holes (PBHs) are present in the cosmic fluid at some instant t=t_0 is investigated. The time t_0 is naturally identified with the end of the inflationary period. The PBHs are assumed to be nonrelativistic in the comoving fluid, to have the same mass, and may be subject to evaporation for t>t_0. Our present work is related to an earlier paper of Zimdahl and Pavon [Phys. Rev. D {\bf 58}, 103506 (1998)], but in contradistinction to these authors we assume that the (negative) production rate of the PBHs is zero. This assumption appears to us to be more simple and more physical. Consequences of the formalism are worked out. In particular, the four-divergence of the entropy four-vector in combination with the second law in thermodynamics show in a clear way how the the case of PBH evaporation corresponds to a production of entropy. Accretion of radiation onto the black holes is neglected. We consider both a model where two different sub-fluids interact, and a model involving one single fluid only. In the latter case an effective bulk viscosity naturally appears in the formalism.