  We consider the linearized semiclassical Einstein equations for small
deviations around de Sitter spacetime including the vacuum polarization effects
of conformal fields. Employing the method of order reduction, we find the exact
solutions for general metric perturbations (of scalar, vector and tensor type).
Our exact (nonperturbative) solutions show clearly that in this case de Sitter
is stable with respect to small metric deviations and a late-time attractor.
Furthermore, they also reveal a breakdown of perturbative solutions for a
sufficiently long evolution inside the horizon. Our results are valid for any
conformal theory, even self-interacting ones with arbitrarily strong coupling.
