Infrared modification of gravity from conformal symmetry

TL;DR

This paper explores a conformal gauge theory of gravity based on the SO(4,2) group, showing it can reproduce Newtonian gravity and potentially explain cosmic acceleration with a renormalizable, conformally invariant framework.

Contribution

It introduces a Yang-Mills type conformal gravity model that unifies local conformal symmetry with gravitational dynamics and links matter couplings to observable gravitational effects.

Findings

Matter coupling to special conformal generators reproduces Newton's law.

Matter coupling to translation generators induces a repulsive force.

The theory's dimensionless coupling suggests potential renormalizability.

Abstract

We reconsider a gauge theory of gravity in which the gauge group is the conformal group SO(4,2) and the action is of the Yang-Mills form, quadratic in the curvature. The resulting gravitational theory exhibits local conformal symmetry and reduces to Weyl-squared gravity under certain conditions. When the theory is linearized about flat spacetime, we find that matter which couples to the generators of special conformal transformations reproduces Newton's inverse square law. Conversely, matter which couples to generators of translations induces a constant and possibly repulsive force far from the source, which may be relevant for explaining the late time acceleration of the universe. The coupling constant of theory is dimensionless, which means that it is potentially renormalizable.