Illuminating the dark universe with gravitational waves

The one thing we know for certain about the dark sector of the universe is that it interacts gravitationally. Gravitational waves are therefore a compelling tool for illuminating its nature. I will discuss prospects for extracting information about dark matter and new fundamental particles from gravitational wave signals, primarily from the space-based gravitational wave detector LISA which was recently adopted by the European Space Agency. I will show the exquisite precision to which we can in principle measure the properties of dark environments around binary black hole systems, as well as present more recent and current work towards how we can do this in practice, utilising simulation-based inference methods to tackle this complex data analysis challenge.