Stability of the semiclassical Einstein equation

The stability of the semiclassical Einstein equation is studied. It is shown that, quite independent of the values of the renormalization parameters, flat spacetime with quantum fields in the Minkowski vacuum is unstable to a certain type of infinitesimal perturbations, and subsequent evolution for these perturbations leads to Planck-scale spacetime curvature in an unacceptably short time scale. This catastrophic evolution is independent of the number of quantum fields in the Universe. For Friedmann spacetimes, such a catastrophe exists, but only for perturbations with finite initial size. For infinitesimal perturbations, the Friedmann spacetimes are stable provided (i) the renormalization parameters are in a certain range and (ii) the back-reaction effects of nonconformal quantum fields are taken into account. The implications of these results are discussed.