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We show how, by considering the cumulative effect of tiny quantum gravitational fluctuations over very large distances, it may be possible to: () reconcile nucleosynthesis bounds on the density parameter of the Universe with the predictions of inflationary cosmology, and () reproduce the inferred variation of the density parameter with distance. Our calculation can be interpreted as a computation of the contribution of quantum gravitational degrees of freedom to the (local) energy density of the Universe.

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