Production of spin-1/2 particles in inhomogeneous cosmologies

The production of spin-1/2 particles by small gravitational inhomogeneities is discussed by using a perturbative approach based on the evaluation of the scattering matrix. We compute the production of massive and massless particles by linear gravitational inhomogeneities in flat spacetime and the production of massless particles in an expanding universe described by the spatially flat Friedmann-Robertson-Walker models with small inhomogeneities. As in the case of scalar particles the total pair-creation probability is given in terms of geometric invariants of the spacetime. © 1992 The American Physical Society.