We describe how a certain simple modification of general relativity, in which the local cosmological constant is allowed to depend on the space-time curvature, predicts the existence of halos of modified gravity surrounding spherically-symmetric objects. We show that the gravitational mass of an object weighed together with its halo can be much larger than its gravitational mass as seen from inside the halo. This effect could provide an alternative explanation of the dark-matter phenomenon in galaxies. In this case, the local cosmological constant in the solar system must be some six orders of magnitude larger than its cosmic value obtained in the supernovae type Ia experiments. This is well within the current experimental bounds, but may be directly observable in the future high-precision experiments.
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