Perturbations of general relativity to all orders and the general nth order terms

A bstract We derive all-order expressions for perturbations of the Einstein-Hilbert action and Einstein equation with general n -th order terms. To this end, we employ Cheung Remmen’s perturbation conventions both in tensor density usual metric formalisms, including Einstein-dilaton theory. Remarkably, find minimal building blocks that generate entire each our formulations. show number terms grows linearly as increases. regard results reference discuss how to other from reference. As a consistency check, compute graviton scattering amplitudes using perturbiner method based on perturbative equation. Finally generalise curved backgrounds incorporate additional matter.