Local Unit Invariance, Back-Reacting Tractors and the Cosmological Constant Problem

TL;DR

This paper explores how conformal geometry and tractor calculus can address the cosmological constant problem by demonstrating how back-reaction naturally stabilizes mass scales and generates scalar potentials, potentially advancing understanding of naturalness issues in cosmology.

Contribution

It introduces tractor stress tensors and shows how back-reaction solves the naturalness problem related to scalar curvature and the cosmological constant, proposing a new geometric approach.

Findings

Back-reaction stabilizes mass scales in conformal geometry.

Scalar fields acquire potentials through classical back-reaction.

A Ricci-flat/CFT correspondence may emerge from tractor calculus.

Abstract

When physics is expressed in a way that is independent of local choices of unit systems, Riemannian geometry is replaced by conformal geometry. Moreover masses become geometric, appearing as Weyl weights of tractors (conformal multiplets of fields necessary to keep local unit invariance manifest). The relationship between these weights and masses is through the scalar curvature. As a consequence mass terms are spacetime dependent for off-shell gravitational backgrounds, but happily constant for physical, Einstein manifolds. Unfortunately this introduces a naturalness problem because the scalar curvature is proportional to the cosmological constant. By writing down tractor stress tensors (multiplets built from the standard stress tensor and its first and second derivatives), we show how back-reaction solves this naturalness problem. We also show that classical back-reaction generates an interesting potential for scalar fields. We speculate that a proper description of how physical systems couple to scale, could improve our understanding of naturalness problems caused by the disparity between the particle physics and observed, cosmological constants. We further give some ideas how an ambient description of tractor calculus could lead to a Ricci-flat/CFT correspondence which generalizes the AdS side of Maldacena's duality to a Ricci-flat space of one higher dimension.