Viability of quadratic gravity, particularly within asymptotically safe quantum gravity

Determine whether four-dimensional quadratic gravity, defined by the Einstein–Hilbert action augmented with quadratic curvature invariants (Weyl-squared and R^2 terms), is a viable theory, particularly within asymptotically safe quantum gravity frameworks.

Background

Quadratic gravity extends general relativity by adding higher-derivative curvature terms, which introduce extra propagating degrees of freedom: a massive scalar and a massive spin-2 mode. The massive spin-2 mode is ghost-like, raising concerns about unitarity and stability when the theory is treated beyond an effective field theory regime.

While quadratic gravity is equivalent to general relativity in vacuum order-by-order within an effective field theory framework via field redefinitions, its status as a complete theory remains unsettled. Asymptotically safe quantum gravity has been proposed as a possible avenue to render such higher-derivative theories consistent, but this has not been conclusively established.

The paper investigates nonperturbative aspects of black hole perturbations and gravitational-wave emission in quadratic gravity, showing exponential suppression of beyond-GR effects in the weak-coupling limit. Nonetheless, the broader question of the theory’s fundamental viability—especially in the asymptotic safety context—remains unresolved.