Viability of quadratic gravity as a realistic quantum gravity framework

Determine whether quadratic gravity, defined by a renormalizable curvature-squared action with R^2 and R^{\mu\nu}R_{\mu\nu} terms (agravity), constitutes a viable and realistic framework for quantum gravity, and ascertain its consistency as a quantum theory across relevant energy scales.

Background

The paper reviews quadratic (curvature-squared) gravity, which improves ultraviolet behavior and renders the theory perturbatively renormalizable, but may introduce ghostlike degrees of freedom and potential unitarity issues. While some works argue for acceptable behavior of scattering amplitudes at ultra-Planckian energies, the overall consistency and realism of quadratic gravity remain debated.

In this context, the authors emphasize that the broader question of the viability of quadratic gravity as a practical and consistent quantum gravity framework is not settled and requires further investigation.

References

The viability of quadratic gravity as a realistic framework for quantum gravity therefore remains an open question requiring additional investigation.

— On the physical running of the electric charge in a dimensionless theory of gravity  (2512.11742 - Gomes et al., 12 Dec 2025) in Introduction (Section 1)

Whether or not additional degrees of freedom result in problems or pathologies remains to be carefully investigated on a case by case basis, as in .

— Emergence of Horndeski gravity from asymptotic safety?  (2609.29369 - Eichhorn et al., 24 Sep 2026) in Section 1, Introduction

This observation has led to our conjecture that the massive ghost might be confined as quarks and gluons in QCD which are controled by the asymptotically free coupling constant as well.

— Massive Ghost Confinement, Dipole Equation and Multipole States in Quadratic Gravity  (2608.26085 - Oda, 26 Aug 2026) in Section 2, paragraph following Eq. (\ref{Couplings})

The four-derivative QG equations have other solutions, like Starobinsky's original inflationary solution, although there has been controversy over the years (starting with ) about whether these inflating solutions, in which the higher-derivative terms dominate at early times, are really self-consistent solutions of semiclassical quantum gravity.

— Might the radiation era extend back to the Big Bang? On dark matter production and the relic graviton background in quadratic gravity  (2609.11750 - Boyle et al., 10 Sep 2026) in Section 2, “Background evolution”