Small Vacuum Energy from Small Equivalence Violation in Scalar Gravity

TL;DR

This paper explores how a small violation of the equivalence principle in scalar gravity, modeled via a CFT deformation and a 6D gauge theory, can naturally lead to an extremely small vacuum energy, addressing the cosmological constant problem.

Contribution

It proposes a novel mechanism linking small equivalence principle violations to tiny vacuum energy via a 6D gauge theory origin within scalar gravity and its CFT dual.

Findings

Small equivalence principle violation leads to exponentially small vacuum energy.

A 6D gauge theory provides a natural origin for the global symmetry protecting pNGBs.

The approach offers insights into non-supersymmetric CFTs in broken phases.

Abstract

The theory of scalar gravity proposed by Nordstr\"{o}m, and refined by Einstein and Fokker, provides a striking analogy to general relativity. In its modern form, scalar gravity appears as the low-energy effective field theory of the spontaneous breaking of conformal symmetry within a CFT, and is AdS/CFT dual to the original Randall-Sundrum I model, but without a UV brane. Scalar gravity faithfully exhibits several qualitative features of the cosmological constant problem of standard gravity coupled to quantum matter, and the Weinberg no-go theorem can be extended to this case as well. Remarkably, a solution to the scalar gravity cosmological constant problem has been proposed, where the key is a very small violation of the scalar equivalence principle, which can be elegantly formulated as a particular type of deformation of the CFT. In the dual AdS picture this involves implementing Goldberger-Wise radion stabilization where the Goldberger-Wise field is a pseudo-Nambu Goldstone boson. In quantum gravity however, global symmetries protecting pNGBs are not expected to be fundamental. We provide a natural six-dimensional gauge theory origin for this global symmetry and show that the violation of the equivalence principle and the size of the vacuum energy seen by scalar gravity can naturally be exponentially small. Our solution may be of interest for study of non-supersymmetric CFTs in the spontaneously broken phase.