Ultralight bosons and supermassive black holes: new fundamental physics from GW observations

Gravitational waves (GW) are opening the possibility of probing otherwise inaccessible physical scenarios, with a transformative impact on our understanding of fundamental physics. One of the most important science cases for GW physics is the discovery of an extension of General Relativity (GR); for example, scalar-tensor theories of gravity beyond GR predict the existence of a scalar mediator of gravity other than the usual tensor interaction. The existence of such scalar fields will have possibly observable effects in Extreme Mass Ratio Inspirals (EMRI), highly-informative astrophysical systems which will be observed by the future GW detector LISA. In this Thesis, I explore the phenomenology of a massive scalar field affecting the EMRI orbital evolution in the perturbative regime, characterizing systematically the effects of the field dynamics using custom analytical and numerical methods. Based on a classical field-theoretical approach, I provide an efficient numerical implementation to compute the field dynamics and its back-reaction on the secondary. I use these results to assess the observability of such effects and forecast the LISA capabilities for estimating the field's parameters. Particular attention is given to the description, modeling, and interpretation of effects specific to massive fields, such as field confinement, global superradiance, and superradiant resonances; for the latter, a thorough investigation of resonant and floating orbits is performed.