Abstract: It is shown that quantum vacuum fluctuations give rise to a curvature of space-time equivalent to a cosmological constant, that is a homogeneous energy density p and pressure p fulfilling - p = p > 0. The fact that the fluctuations produce curvature, even if the vacuum expectation of the energy vanishes, is a consequence of the non-linear character of the Einstein equation. A calculation is made, involving plausible hypotheses within quantized gravity, which establishes a relation between the two-point correlation of the vacuum fluctuations and the space-time curvature. Arguments are given which suggest that the density p might be of order the "dark energy" density currently assumed to explain the observed accelerated expansion of the universe.

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