Renormalizability and Newtonian potential in scale-invariant gravity

TL;DR

This paper demonstrates that scale-invariant gravity (SIG) is renormalizable, exhibits improved ultraviolet behavior, and produces a linear classical potential, making it a UV complete theory.

Contribution

The work shows that SIG satisfies the conjecture of finite potential at the origin and has a $1/k^4$ UV behavior, establishing its renormalizability and UV completeness.

Findings

SIG has a $1/k^4$ UV behavior.

SIG produces a linear classical potential $V\propto r$.

SIG is a UV complete theory.

Abstract

There is a conjecture that renormalizable higher-derivative gravity has a finite classical potential at the origin. In this work we show clearly that the scale-invariant gravity (SIG) satisfies the conjecture. This gravity produces the better-behaved $1/k^4$ UV behavior as needed for renormalizability. It turns out that the SIG has the linear classical potential of $V\propto r$ and it is a UV complete theory.