Effective Field Theory Methods in Gravitational Physics and Tests of Gravity

TL;DR

This thesis applies effective field theory methods to gravitational physics, exploring scalar-tensor theories, renormalization of energy-momentum tensors, and proposing new frameworks for testing General Relativity with gravitational waves.

Contribution

It introduces a novel EFT-based framework for analyzing gravitational interactions and testing gravity in strong-field regimes using gravitational wave data.

Findings

Renormalization of energy-momentum tensor for point-like and string-like sources.

Constraints on three-graviton vertex from pulsar data at 0.1% level.

Potential to constrain higher-order graviton vertices with future gravitational wave observations.

Abstract

In this PhD thesis I make use of the "Effective Field Theory of Gravity for Extended Objects" by Goldberger and Rothstein in order to investigate theories of gravity and to take a different point of view on the physical information that can be extracted from experiments. In the first work I present, I study a scalar-tensor theory of gravity and I address the renormalization of the energy-momentum tensor for point-like and string-like sources. The second and third study I report are set in the context of testing gravity. So far experiments have probed dynamical regimes only up to order (v/c)^5 in the post-Newtonian expansion, which corresponds to the very first term of the radiative sector in General Relativity. In contrast, by means of gravitational-wave astronomy, one aims at testing General Relativity up to (v/c)^(12)! It is then relevant to envisage testing frameworks which are appropriate to this strong-field/radiative regime. In the last two chapters of this thesis a new such framework is presented. Using the effective field theory approach, General Relativity non-linearities are described by Feynman diagrams in which classical gravitons interact with matter sources and among themselves. Tagging the self-interaction vertices of gravitons with parameters it is possible, for example, to translate the measure of the period decay of Hulse-Taylor pulsar in a constraint on the three-graviton vertex at the 0.1% level; for comparison, LEP constraints on the triple-gauge-boson couplings of weak interactions are accurate at 3%. With future observations of gravitational waves, higher order graviton vertices can in principle be constrained through a Fisher matrix analysis.