Higher-Derivative Theories of Gravity

Dear Colleagues,

A vast amount of observational data have made Einstein's General Relativity (GR) the best current theory that describes classical aspects of the gravitational interaction. However, despite its great success, there are still fundamental questions that remain unanswered. On short-distance scales, GR predicts the existence of black-hole and cosmological big-bang singularities where spacetime terminates and the theory breaks down. Moreover, Einstein's theory lacks predictability in the high-energy regime, being perturbatively non-renormalizable.

A natural way to extend GR in the high-energy and short-distance regimes is to generalize the Einstein–Hilbert Lagrangian by adding higher powers of the curvature tensors. Indeed, in 1977, Kellogg Stelle showed that quadratic curvatures are sufficient to formulate a renormalizable theory of quantum gravity. However, such additional terms were also shown to introduce a “ghost” degree of freedom because of higher-order time-derivatives that cause classical Hamiltonian instabilities and break unitarity at the quantum level. This moment in the history of Theoretical Physics—more than forty years ago—can be considered to be the beginning of many new attempts aimed at formulating a consistent quantum theory of gravity, and thus at solving both issues of the renormalizability and unitarity of the gravitational interaction.

The aim of this Special Issue is to present a collection of original research and review articles on different approaches to quantum gravity by placing particular emphasis on the role and true meaning of higher, or even infinite, derivatives in the quantization of the gravitational interaction. Both formal aspects and applications of higher-derivative theories will be covered.

Dr. Luca Buoninfante
Prof. Dr. Gaetano Lambiase
Guest Editors

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• higher derivatives
• ghosts and unitarity
• nonlocal field theories
• quantum gravity
• astrophysical and cosmological applications of higher-derivative gravity