Conformal symmetry of gravity and the cosmological constant problem

TL;DR

This paper explores a conformally invariant formulation of gravity that could explain the small observed value of the cosmological constant by linking it to matter coupling and symmetry considerations.

Contribution

It derives a conformal field theory description of gravity with a novel stress-energy tensor and discusses how matter coupling breaks conformal symmetry, impacting the cosmological constant.

Findings

Conformal symmetry constrains the vacuum energy to be zero.

The physical cosmological constant arises from matter coupling.

The model describes a flat FRW universe within a conformal gravity framework.

Abstract

In absence of matter Einstein gravity with a cosmological constant $\La$ can be formulated as a scale-free theory depending only on the dimensionless coupling constant G \Lambda where G is Newton constant. We derive the conformal field theory (CFT) and its improved stress-energy tensor that describe the dynamics of conformally flat perturbations of the metric. The CFT has the form of a constrained \lambda \phi^{4} field theory. In the cosmological framework the model describes the usual Friedmann-Robertson-Walker flat universe. The conformal symmetry of the gravity sector is broken by coupling with matter. The dimensional coupling constants G and \Lambda are introduced by different terms in this coupling. If the vacuum of quantum matter fields respects the symmetry of the gravity sector, the vacuum energy has to be zero and the ``physical'' cosmological constant is generated by the coupling of gravity with matter. This could explain the tiny value of the observed energy density driving the accelerating expansion of the universe.