  We propose a criterion for the validity of semiclassical gravity (SCG) which
is based on the stability of the solutions of SCG with respect to quantum
metric fluctuations. We pay special attention to the two-point quantum
correlation functions for the metric perturbations, which contain both
intrinsic and induced fluctuations. These fluctuations can be described by the
Einstein-Langevin equation obtained in the framework of stochastic gravity.
Specifically, the Einstein-Langevin equation yields stochastic correlation
functions for the metric perturbations which agree, to leading order in the
large $N$ limit, with the quantum correlation functions of the theory of
gravity interacting with $N$ matter fields. The homogeneous solutions of the
Einstein-Langevin equation are equivalent to the solutions of the perturbed
semiclassical equation, which describe the evolution of the expectation value
of the quantum metric perturbations. The information on the intrinsic
fluctuations, which are connected to the initial fluctuations of the metric
perturbations, can also be retrieved entirely from the homogeneous solutions.
However, the induced metric fluctuations proportional to the noise kernel can
only be obtained from the Einstein-Langevin equation (the inhomogeneous term).
These equations exhibit runaway solutions with exponential instabilities. A
detailed discussion about different methods to deal with these instabilities is
given. We illustrate our criterion by showing explicitly that flat space is
stable and a description based on SCG is a valid approximation in that case.
