Improved Positivity Bounds and Massive Gravity
  Theories such as massive Galileons and massive gravity can satisfy the
presently known improved positivity bounds provided they are weakly coupled. We
discuss the form of the EFT Lagrangian for a weakly coupled UV completion of
massive gravity which closely parallels the massive Galileon, and perform the
power counting of corrections to the scattering amplitude and the positivity
bounds. The Vainshtein mechanism which is central to the phenomenological
viability of massive gravity is entirely consistent with weak coupling since it
is classical in nature. We highlight that the only implication of the improved
positivity constraints is that EFT cutoff is lower than previous assumed, and
discuss the observable implications, emphasizing that these bounds are not
capable of ruling out the model contrary to previous statements in the
literature.
