Renormalizability and Newtonian potential in scale-invariant gravity

Understand

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.