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

TL;DR

The paper demonstrates how NRGR-inspired EFT methods apply to a scalar gravity model to compute the 1PN EIH action, illustrating a systematic perturbative framework for post-Newtonian corrections. By decomposing modes and performing power counting, it reveals how self-interactions (λ) and a scalar mass μ influence the expansion and lead to specific corrections, including a log potential. The results show that in pure scalar gravity non-derivative self-interactions are highly constrained, while extensions to scalar-tensor theories require either very small couplings or new high-scale physics to remain viable. Overall, the work highlights a robust methodology for PN analyses and for constraining alternative gravitational couplings using EFT concepts.

Abstract

The problem of motion in General Relativity has lost its academic status and become an active research area since the next generation of gravity wave detectors will rely upon its solution. Here we will show, within scalar gravity, how ideas borrowed from Quantum Field Theory can be used to solve the problem of motion in a systematic fashion. We will concentrate in Post-Newtonian corrections. We will calculate the Einstein-Infeld-Hoffmann action and show how a systematic perturbative expansion puts strong constraints on the couplings of non-derivative interactions in the theory.

Figures (2)

• Figure 1: One s-graviton exchange contribution at 1PN. The $\bigotimes$ represents a correction to the propagator, and $\times$ a mass insertion.
• Figure 2: Non linear contributions at 1PN.