Abstract: It is assumed that, for weak space-time curvature, the main gravitational effect of the quantum vacuum stress energy corresponds to adding two terms to the Einstein-Hilbert action, proportional to the square of the curvature scalar and to the contraction of two Ricci tensors, respectively. It is shown that compatibility with terrestrial and Solar System observations implies that the square roots of the coefficients of these terms should be either a few millimeters or a few hundred meters. It is shown that the vacuum contribution increase the stability of massive white dwarfs.

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