Degravitation and the relaxed Einstein equations

TL;DR

This paper proposes a covariant modification to Einstein's equations by replacing G with a differential operator to degravitate vacuum energy, deriving effective equations and analyzing post-Newtonian limits.

Contribution

It introduces a covariant coupling model acting as a high-pass filter to modify Einstein's equations and derives the effective relaxed equations and near-zone mass in this framework.

Findings

Recovers general relativity results in the limit of no modification.

Derives effective relaxed Einstein equations for the modified theory.

Analyzes the post-Newtonian total mass in a many-body system.

Abstract

The general idea to modify Einstein's field equations by promoting Newton's constant $G$ to a covariant differential operator $G_\Lambda(\Box_g)$ was apparently outlined for the first time in [12-15]. The modification itself originates from the quest of finding a mechanism which is able to degravitate the vacuum energy on cosmological scales. We present in this article a precise covariant coupling model which acts like a high-pass filter with a macroscopic distance filter scale $\sqrt{\Lambda}$. In the context of this particular theory of gravity we work out the effective relaxed Einstein equations as well as the effective 1.5 post-Newtonian total near-zone mass of a many body system. We observe that at any step of computation we recover in the limit of vanishing modification parameters the corresponding general relativistic result.