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Higher derivative theories of gravity: problems of unitarity and renormalizzability

Lezioni di dottorato
2021-11-12 10:00 - 12:00
Microsoft Teams
Tokyo Institute of Technology
Area di Ricerca
2021-11-12 10:00:00
A vast amount of observational data has 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 K. 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. In this course we will review the issues of renormalizability, higher derivatives and unitarity in formulating a consistent quantum field theory of the gravitational interaction. After introducing the main problems of perturbative quantum gravity, we will explore several recent alternative theories of gravity involving higher (or even infinite) derivatives. We will mainly study perturbations around the Minkowski background and perform explicit computations, e.g. of graviton propagators, vertexes, amplitudes, metric potentials etc. In addition to analyse formal aspects of such gravitational theories, we will also discuss applications in astrophysics and cosmology.

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