Generalized Schwinger effect and particle production in an expanding universe

We discuss several aspects of particle production in (a) a time-dependent electric field and (b) an expanding Friedmann background. In the first part of the paper, we provide an algebraic mapping between the differential equations describing these two phenomena. This mapping allows a direct comparison between a and b, and we highlight several interesting features of both cases using this approach. We determine the form of the (equivalent) electric field corresponding to different Friedmann spacetimes and discover, e.g., a time-dependent electric field, which, in a specific limit, leads to a Planck spectrum of particles. We also discuss the conditions under which the particle production in an expanding background will be nonanalytic in the parameter which encodes the coupling to the curved spacetime, in close analogy with the generalized Schwinger effect. In the second part of the paper, we study the situation in which both a time-dependent electric field and an expanding background are simultaneously present. We compute particle production rate in this context by several different methods, paying special attention to its limiting forms and possible nonanalytic behavior. We also clarify several conceptual issues related to definitions of in vacuum and out vacuum in these systems.