Abstract
A scheme for solving the semiclassical back-reaction equations for free quantum fields in curved spacetime is proposed. The quantum fields can have arbitrary masses and arbitrary couplings to the curvature. All back-reaction effects including vacuum polarizations can be taken into account. The scheme has been applied successfully to the reheating calculations of the Starobinsky-type inflationary models. The damping of the oscillation in curvature and the reheating of the Universe are seen explicitly.