  A new analysis of extended data records collected with the Lunar Laser
Ranging (LLR) technique performed with improved tidal models was not able to
resolve the issue of the anomalous rate $\dot e$ of the eccentricity $e$ of the
orbit of the Moon, which is still in place with a magnitude of $\dot e=(5\pm
2)\times 10^{-12}$ yr$^{-1}$. Some possible cosmological explanations are
offered in terms of the post-Newtonian effects of the cosmological expansion,
and of the slow temporal variation of the relative acceleration rate $\ddot{S}
S^{-1}$ of the cosmic scale factor $S$. None of them is successful since their
predicted secular rates of the lunar eccentricity are too small by several
orders of magnitude.
