Nonlocal Spacetime-Matter

Abstract: We propose a nonlocal field theory for gravity in presence of matter consistent with perturbative unitarity, quantum finiteness, and other essential classical properties that we are going to list below. First, the theory exactly reproduces the same tree-level scattering amplitudes of Einstein's gravity coupled to matter insuring no violation of macro-causality. Second, all the exact solutions of the Einstein's theory are also exact solutions of the nonlocal theory. Finally, and most importantly, the linear and nonlinear stability analysis of the exact solutions in nonlocal gravity (with or without matter) is in one to one correspondence with the same analysis in General Relativity. Therefore, all the exact solutions stable in the Einstein's theory are also stable in nonlocal gravity in presence of matter at any perturbative order.