The “Cosmology and Fundamental Physics with Gravitational Waves” work package focuses on aspects of fundamental physics that we either need to further develop in order to extract knowledge from the next-generation GW observatories’ data, or we believe we can constrain by using these data. Independently of the techniques used to extract signal from the noisy gravitational-wave data streams, a library of accurate waveforms, spanning the parameter space of the astrophysical properties of potential gravitational-wave sources, is required. In both LISA and ET, many very high SNR detections are expected. Thus, the required accuracy of waveforms, which scales with SNR, significantly exceeds that of existing ones. The second goal of this work-package is to study the nature of dark energy and dark matter through GWs, employing machine-learning and statistical inference techniques.