NLQG · Understanding NonLocality in Quantum Gravity

Understanding NonLocality in Quantum Gravity

A vast amount of observational data has confirmed the theoretical predictions of Einstein's General Relativity (GR), making it the currently best known theory to describe classical aspects of the gravitational interaction, from cosmological to sub-millimeter scales. Despite this phenomenal success, there are still fundamental questions that remain unanswered. At small scales, GR predicts the existence of singularities in black holes and at the big bang, where the theory breaks down. At the quantum level, Einstein's theory lacks predictivity in the ultraviolet regime, i.e., at high energies, as it is perturbatively non-renormalizable. It is generally believed that a consistent theory of quantum gravity is needed to address these challenges. In the last decades, new theoretical progress has been made toward developing quantum gravity approaches and gaining new insights into quantum aspects of gravity. Despite their intrinsic differences, most of these approaches describe new physics in the high-energy regime via additional higher-curvature invariants containing finite-order (i.e. local) and/or non-polynomial (i.e. non-local) differential operators, which can appear in the gravitational Lagrangian at effective and fundamental levels. These operators are known as form factors. Higher derivative field theories often introduce "ghost" degrees of freedom which are sometimes considered responsible for classical instabilities (due to negative energies) and violation of S-matrix unitarity at the quantum level. However, in recent years the field of higher-derivative gravity has had a renaissance as new ideas for instability-free, unitary quantizations of ghost fields have been proposed in the case of local gravitational Lagrangians, while the existence of ghost-free form factors has been demonstrated for non-local Lagrangians. This means that it is now possible to formulate quantum field theories (QFTs) of gravity which are perturbatively stable and unitary despite the presence of higher-derivative form factors. A full derivation of the form factors in the quantum-gravity Lagrangian is still pending in the known approaches and scenarios mentioned above. Moreover, when the locality principle is given up, it becomes difficult to uniquely select the Lagrangian because there exists an infinite class of ghost-free gravity models whose non-polynomial form factors are such that no ghost appears. This means that from a bottom-up point of view additional constraints are needed to reduce the degeneracy. The overall goal of this project has been twofold: (i) to derive and enforce fundamental consistency requirements of causality, stability, unitarity, and healthy high-energy behavior in order to constrain the space of allowed gravitational QFTs; (ii) to use experimental constraints inferred from astrophysical and cosmological observations to further test and constrain the quantum-gravity Lagrangian.

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