Testing nonlocal gravity with Lunar Laser Ranging
  We study the impact of the limit on $|\dot{G}|/G$ from Lunar Laser Ranging on
"nonlocal gravity", i.e. on models of the quantum effective action of gravity
that include nonlocal terms relevant in the infrared, such as the "RR" and "RT"
models proposed by our group, and the Deser-Woodard (DW) model. We elaborate on
the analysis of Barreira et al. [1] and we confirm their findings that (under
plausible assumptions such as the absence of strong backreaction from
non-linear structures), the RR model is ruled out. We also show that the
mechanism of "perfect screening for free" suggested for the DW model actually
does not work and the DW model is also ruled out. In contrast, the RT model
passes all phenomenological consistency tests and is still a viable candidate.
