Effective Field Theory and Applications

In this chapter, we will review the field-theoretic treatment of general relativity based on an effective field theory extension of the Einstein-Hilbert action. This pragmatic route to low-energy quantum effects in gravity critically underpins miscellaneous investigations of phenomenological and quantum extensions of general relativity. We discuss how it allows quantum field theory to be a theoretical laboratory for testing Einstein’s theory of gravity. We also demonstrate the current state of an efficient and practical scheme for evaluating the classical components of perturbative weak field scattering amplitudes until the fourth post-Minkowskian order. Such results complement numerical predictions in Einstein’s theory of gravity.