Effect of particle production in Robertson-Walker spacetime

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.