  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 to
perform several fine tests of the relativistic gravitational field theory
(General Relativity). Yet another promising application of LLR arises just now
in the context of recent cosmological models, whose dynamics is substantially
affected by some kinds of the dark matter (or the so-called "dark energy")
uniformly distributed in space, and therefore should be accompanied by some
residual Hubble expansion at any spatial scales, particularly, in the
Earth-Moon system. The "local" Hubble expansion can be revealed by comparing
the rate of increase in the lunar semi-major axis measured by LLR (which should
be produced both by the well-known tidal exchange of angular momentum between
the Earth and Moon and the local Hubble expansion) with the same quantity
derived indirectly from astrometric data on the Earth's rotation deceleration
(which is produced only by the tidal interaction). Such analysis really points
to the discrepancy 1.3 cm/yr, which corresponds to the local Hubble constant
H_0^(loc) = 33 +/- 5 (km/s)/Mpc. This value is about two times less than at
intergalactic scales but many orders of magnitude greater than was predicted in
earlier theoretical works.
