  Linearized fluctuations of quantized matter fields and the spacetime geometry
around de Sitter space are considered in the case that the matter fields are
conformally invariant. Taking the unperturbed state of the matter to be the de
Sitter invariant Bunch-Davies state, the linear variation of the stress tensor
about its self-consistent mean value serves as a source for fluctuations in the
geometry through the semi-classical Einstein equations. This linear response
framework is used to investigate both the importance of quantum backreaction
and the validity of the semi-classical approximation in cosmology. The full
variation of the stress tensor, delta T^a_b contains two kinds of terms: (1)
those that depend explicitly upon the linearized metric variation delta g_{cd}
through the [T^a_b, T^{cd}] causal response function; and (2) state dependent
variations, independent of delta g_{cd}. For perturbations of the first kind,
the criterion for the validity of the semi-classical approximation in de Sitter
space is satisfied for fluctuations on all scales well below the Planck scale.
The perturbations of the second kind contain additional massless scalar degrees
of freedom associated with changes of state of the fields on the cosmological
horizon scale. These scalar degrees of freedom arise necessarily from the local
auxiliary field form of the effective action associated with the trace anomaly,
are potentially large on the horizon scale, and therefore can lead to
substantial non-linear quantum backreaction effects in cosmology.
