Non‑perturbative stability of quadratic and non‑local gravity

Investigate whether non‑perturbative and classical instabilities occur in quadratic‑curvature gravity and in ghost‑free non‑local gravity, despite perturbative indications of stability, and determine conditions under which these theories are stable.

Background

Quadratic gravity and non‑local gravity can avoid perturbative pathologies and appear stable at that level. However, their non‑perturbative and classical behavior may differ.

The panel explicitly recognized uncertainty about potential instabilities beyond perturbation theory, highlighting the need for rigorous non‑perturbative analyses.

References

In both cases, while the stability of the theory seems to be under control at the perturbative level, it was remarked that it is still unclear whether instabilities can arise non-perturbatively and in the classical limit.

— Visions in Quantum Gravity  (2412.08696 - Buoninfante et al., 2024) in Panel 2 (Subsection "Unitarity, causality, stability")

We ignore the controversial debate regarding whether an undesirable growth of the scalar part of the ghost perturbation in the superhorizon regime is a gauge artifact or not .

— Dark matter in scale-invariant gravity with hidden-sector condensation  (2608.12456 - Garcés et al., 12 Aug 2026) in Section 2.2, subsection “Inflationary parameters,” footnote following Eq. (ratio)

Several questions remain open. A complete spectral analysis including the massive modes present in theories with quadratic curvature invariants would go beyond the radion sector considered here.

— Continuum Landscape of stable extra-dimensional metrics  (2610.08006 - Rubin, 6 Oct 2026) in Section 7, “Conclusion”

A number of investigations were devoted also to non integrable systems, although the issue of quantum stability is still open.

— Can we make sense out of negative kinetic energy?  (2610.10040 - Maiezza et al., 7 Oct 2026) in Section 1, Introduction