Quadratic Gravity

TL;DR

Quadratic gravity, which adds curvature-squared terms to Einstein's theory, is renormalizable but introduces ghosts; recent progress explores its stability, renormalization, and potential as a UV complete theory.

Contribution

This paper reviews quadratic gravity's renormalization, stability issues, and the role of renormalization group flows, offering new insights into its viability as a fundamental theory.

Findings

Quadratic gravity is renormalizable with a ghost issue due to higher derivatives.

Stability of higher derivative theories has recent progress.

Renormalization group equations allow extrapolation to infinite energy if matter couplings reach fixed points.

Abstract

Adding terms quadratic in the curvature to the Einstein-Hilbert action renders gravity renormalizable. This property is preserved in the presence of the most general renormalizable couplings with (and of) a generic quantum field theory (QFT). The price to pay is a massive ghost, which is due to the higher derivatives that the terms quadratic in the curvature imply. In this paper the quadratic gravity scenario is reviewed including recent progress on the related stability problem of higher derivative theories. The renormalization of the theory is also reviewed and the final form of the full renormalization group equations in the presence of a generic renormalizable QFT is presented. The theory can be extrapolated up to infinite energy through the renormalization group if all matter couplings flow to a fixed point (either trivial or interacting). Moreover, besides reviewing the above-mentioned topics some further insight on the ghost issue and the infinite energy extrapolation is provided. There is the hope that in the future this scenario might provide a phenomenologically viable and UV complete relativistic field theory of all interactions.