Partial creation in de Sitter spacetime is studied in a complex-time WKB approximation. It is found that the particle production parallels the description of particle creation by a collapsing spherical body. The appropriate vacuum for an inflationary early universe is the Hartle--Hawking vacuum; this is also a general feature of expanding spacetimes. The effect of particle production back on the metric is treated in a way that differs from the standard semiclassical approach.

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We show that the Dirac equation in Robertson--Walker (RW) spacetime can be written in a two-dimensional equivalent form that parallels the motion of an electron in a time-varying electric field. Using the effect of particle production, a RW spacetime that describes a universe which contracts and re-expands almost symmetrically and becomes asymptotically static is simulated. The back-reaction problem is considered only through the quantum behaviour of particle production without any reference to Einstein field equations.

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The definition of vacuum in curved space-time is a delicate object. With Minkowskilike vacuum definition, the current has a characteristic behavior in Robertson-Walker space-time. In this work we study the behavior of Dirac current in a de Sitter spacetime. The rapid oscillations of current is observed with respect to time and indicate vigorous instability in initial vacuum and is interpreted as vigorous particle production.

We study the behaviour of Dirac current in expanding spacetime with Schrödinger and de Sitter form for the evolution of the scale-factor. The study is made to understand the particleantiparticle rotation and the evolution of quantum vacuum leading to particle production in such spacetime.