  Stochastic backgrounds of gravitational waves are intrinsic fluctuations of
spacetime which lead to an unavoidable decoherence mechanism. This mechanism
manifests itself as a degradation of the contrast of quantum interferences. It
defines an ultimate decoherence border for matter-wave interferometry using
larger and larger molecules. We give a quantitative characterization of this
border in terms of figures involving the gravitational environment as well as
the sensitivity of the interferometer to gravitational waves. The known level
of gravitational noise determines the maximal size of the molecular probe for
which interferences may remain observable. We discuss the relevance of this
result in the context of ongoing progresses towards more and more sensitive
matter-wave interferometry.
