Testing general relativity with gravitational waves from extreme mass-ratio inspirals

Extreme Mass Ratio Inspirals (EMRIs) are asymmetric binary systems. They are composed of a massive black hole and a stellar mass compact object, which inspirals until the plunge, emitting gravitational waves (GWs) potentially observable by future space based detectors, such as the Laser Interferometer Space Antenna (LISA). In the final year before the plunge, EMRIs complete thousands of cycles in the strong-field region around the massive black hole. Tracking such large number of orbits would allow to measure the source parameters with exquisite accuracy, and to perform precise strong-field tests of gravity. Following such quest and exploiting the scientific potential of asymmetric binaries require accurate waveforms in modified theories of gravity, to compare against General Relativity (GR) predictions. Such models are currently missing, due to the complexity of calculations beyond GR. In this thesis we provide a key step forward, and discuss the modelling of EMRIs when the gravitational interaction is mediated by additional fundamental fields. We develop a new theoretical framework able to describe the EMRI dynamical evolution in a vast class of modified theories of gravity with extra massless and massive scalar fields. Exploiting decoupling of scales we show how, at leading order in the binary mass ratio, deviations from GR for the massive BH can be neglected such that the background spacetime can be described by the Kerr metric. In this approach all information about the underlying gravity theory is encoded by the scalar charge of the inspiralling lighter body, and by the mass of the scalar field. These two parameters fully capture the imprint of the scalar field on the emitted gravitational waves. We perform an extensive data analysis of mock GW signals emitted by asymmetric binaries, forecasting LISA ability to constrain the scalar field parameters. Our results show that EMRIs provide golden sources to probe the existence of new fundamental fields in the Universe.