  We study positivity bounds in the presence of gravity. We first review the
gravitational positivity bound at the tree-level, where it is known that a
certain amount of negativity is allowed for the coefficients of
higher-derivative operators. The size of these potentially negative
contributions is estimated for several tree-level, Reggeized gravitational
amplitudes which are unitary at high energies and feature the t-channel pole
characteristic of graviton exchange. We also argue for the form of the one-loop
Regge amplitude assuming that the branch cut structure associated with the
exchange of the graviton and higher-spin particles is reflected. We demonstrate
how the one-loop Regge amplitude appears by summing over Feynman diagrams. For
our one-loop amplitude proposal, the positivity bounds generically receive a
finite contribution from the Regge tower and do not lead to a parametrically
small bound on the cut-off scale of the low-energy EFT, consistent with recent
studies based on sum rules of the amplitude.
