  The two-point function characterizing the stress tensor fluctuations of a
massless minimally coupled field for an invariant vacuum state in de Sitter
spacetime is discussed. This two-point function is explicitly computed for
spacelike separated points which are geodesically connected. We show that these
fluctuations are as important as the expectation value of the stress tensor
itself. These quantum field fluctuations will induce fluctuations in the
geometry of de Sitter spacetime. This paper is a first step towards the
computation of such metric fluctuations, which may be of interest for
large-scale structure formation in cosmology. The relevance of our results in
this context is briefly discussed.
