Causality and Scattering Amplitudes in Nonlocal Gravity

A remarkable feature of weakly nonlocal gravitational theories (eventually coupled to matter), which are compatible with perturbative unitarity and finiteness at quantum level, is that they exhibit the same tree-level scattering amplitudes as Einstein’s gravity. After reviewing the explicit computation for the four-graviton scattering amplitude and a general proof for n-point amplitudes based on a field redefinition, we show as a consequence that in nonlocal quantum gravity, a Shapiro’s time advance, which is related to a violation of macro-causality, never occurs. Moreover, we provide a recipe to construct a general ultraviolet complete gravitational theory coupled to matter compatible with macro-causality. Finally, we present similar results for local Lee-Wick quantum gravity, whereas we highlight that nonlocal gravity in Weyl basis can potentially violate causality.