Scalar gravity: Post-newtonian corrections via an effective field theory approach

Abstract

This chapter shows how an effective field theory (EFT) approach can be used to solve the problem of motion in a systematic fashion within scalar gravity. The EFT approach is a powerful tool within the PN framework. The power of the EFT formalism resides in a manifest power counting in the expansion parameter of the theory. The Einstein-Infeld-Hoffmann (EIH) action for the case of two scalar-gravitating bodies is calculated accurately up to 1PN. The leading order one s-graviton exchange can be shown to reproduce Newtonian gravity. A systematic perturbative expansion puts strong constraints on the couplings of non-derivative interactions in the theory. The NRGR power counting rules prove that in order to produce a well defined perturbative expansion, the self interaction (λ) had to be fine tuned to a ridiculously small scale.