The lingering anomalous secular increase of the eccentricity of the   orbit of the Moon: further attempts of explanation of cosmological origin
  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. 
Lorenzo Iorio
gr-qc astro-ph.EP physics.geo-ph physics.space-ph