Riemann-Eddington theory: Incorporating matter, degravitating the cosmological constant

TL;DR

This paper extends Eddington's affine gravity with Riemann curvature to incorporate matter and proposes a natural, local mechanism for degravitation of the cosmological constant through a hierarchy of gravitational constants.

Contribution

It introduces a novel Riemann-Eddington gravity framework where vacuum gravitates differently, enabling degravitation without fine-tuning, based on a hierarchy of gravitational constants.

Findings

Matter couples to gravity as in standard theories.

Vacuum gravitates with a different, independent gravitational constant.

Degravitation of the cosmological constant is achieved naturally and locally.

Abstract

Here we show that, Eddington's pure affine gravity, when extended with Riemann curvature, leads to gravitational field equations that incorporate matter. This Riemanned Eddington gravity outfits a setup in which matter gravitates normally with Newton's constant but vacuum gravitates differently with an independent gravitational constant. This novel setup enables degravitation of the vacuum to observed level not by any fine-tuning but by a large hierarchy between its gravitational constant and its energy density. Remarkably, degravitation of the cosmological constant is local, causal and natural yet only empirical because the requisite degravitation condition is not predicted by the theory.