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A new analysis of extended data records collected with the Lunar LaserRanging (LLR) technique performed with improved tidal models was not able toresolve the issue of the anomalous rate $\dot e$ of the eccentricity $e$ of theorbit of the Moon, which is still in place with a magnitude of $\dot e=(5\pm2)\times 10^{-12}$ yr$^{-1}$. Some possible cosmological explanations areoffered 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 theirpredicted secular rates of the lunar eccentricity are too small by severalorders of magnitude.

The lingering anomalous secular increase of the eccentricity of the orbit of the Moon: further attempts of explanation of cosmological origin