Renormalization of a modified gravity with a quadratic Riemann tensor term

TL;DR

This paper explores a modified gravity theory with a quadratic Riemann tensor term, showing it shares topological and divergence properties with Yang-Mills theories, leading to the conclusion of its renormalizability.

Contribution

It introduces a gravity model with an affine connection independent of the metric and demonstrates its renormalizability by analogy with Yang-Mills theories.

Findings

In the low density limit, it reduces to General Relativity.

The metric does not contribute propagators or quantum fluctuations.

The theory's Feynman diagrams share topology with Yang-Mills theories.

Abstract

We consider a modified form of gravity, which has an extra term quadratic in the Riemann tensor. This term mimics a Yang-Mills theory. The other defining characteristic of this gravity is having the affine connection independent of the metric. (The metricity of the metric is rejected, too, since it implies a Levi-Civita connection.) It is then shown that, in the low density limit, this modified gravity does not differ from the General Theory of Relativity. We then point out that its Lagrangian does not contain partials of the metric, so that the metric is not a quantum field, nor does it contribute propagators to the Feynman diagrams of the theory. We also point out that the couplings of this theory (that determine the topological structure of the Feynman diagrams) all come from the term quadratic in the Riemann tensor. As a result of this situation, the diagrams of this theory and the diagrams of a Yang-Mills theory all have the same topology and degree of divergence, up to numerical coefficients. Since Yang-Mills theories are renormalizable, it follows that this theory should also be renormalizable.