Higher-curvature corrections in black holes and the early universe through gravitational wave observations

General Relativity (GR) is broadly accepted as the correct description of the gravitational interaction when the curvature of spacetime is relatively low, but modifications of this theory are expected to arise at high energies. In an effective-field-theory approach, such modifications can be captured by introducing higher-curvature corrections in the Einstein's field equations. There has been a great interest in the literature in order to understand the role of these corrections in black hole solutions and in the very early universe, but there are still open questions that we intend to address in this project.   First, there are no examples of non-perturbative rotating black hole solutions with higher-curvature corrections, and we aim to provide the first one. Second, the role of general higher-curvature corrections during cosmic inflation is not understood, and we wish to study, in particular, how they affect the well-known Starobinsky model.  Finally, for the first time we are going to measure the properties of astrophysical black holes thanks to the gravitational wave detectors LIGO/Virgo and the Event horizon telescope. This opens up the possibility of detecting higher-curvature corrections in black holes through gravitational wave observations, but in order to achieve this goal it is necessary to determine the prediction of these theories for observable quantities, such as the quasinormal modes of black holes.