Precise measurements of the Earth-Moon distance by the lunar laser ranging(LLR), which begun in the early 1970's, contributed significantly to geodesy,geophysics, and lunar planetology, as well as enabled astrophysicists toperform several fine tests of the relativistic gravitational field theory(General Relativity). Yet another promising application of LLR arises just nowin the context of recent cosmological models, whose dynamics is substantiallyaffected by some kinds of the dark matter (or the so-called "dark energy")uniformly distributed in space, and therefore should be accompanied by someresidual Hubble expansion at any spatial scales, particularly, in theEarth-Moon system. The "local" Hubble expansion can be revealed by comparingthe rate of increase in the lunar semi-major axis measured by LLR (which shouldbe produced both by the well-known tidal exchange of angular momentum betweenthe Earth and Moon and the local Hubble expansion) with the same quantityderived indirectly from astrometric data on the Earth's rotation deceleration(which is produced only by the tidal interaction). Such analysis really pointsto the discrepancy 1.3 cm/yr, which corresponds to the local Hubble constantH_0^(loc) = 33 +/- 5 (km/s)/Mpc. This value is about two times less than atintergalactic scales but many orders of magnitude greater than was predicted inearlier theoretical works.
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