The field of gravitational-wave (GW) astronomy has been revolutionized by the discovery of GWs from compact binary inspirals by LIGO and the identification of a stochastic background by pulsar timing arrays. These groundbreaking discoveries have not only opened new windows into astrophysics and cosmology, but have also posed many profound questions. From unraveling the astrophysical origins of compact inspiral systems and their utility in measuring the Universe's expansion rate to exploring the exotic realms of primordial black holes, the research spectrum is vast and vibrant.

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Additionally, the stochastic background of GWs hints at the mergers of supermassive black holes and could provide constraints on vestiges of early universe phenomena, offering a unique lens through which to probe the origins of supermassive black holes and their role in the evolution of galaxies. The field is advancing at a remarkable pace, fueled by the advent of new ground-based and space-based observatories, promising a future filled with discovery and innovation in our quest to understand some of the Universe's most elusive phenomena.

Future GW detectors will improve in sensitivity by at least an order of magnitude and the redshift range of accessible sources will extend by several orders. To match this progress on the experimental side, requires accurate theoretical predictions of the signals. In particular, the inspiral phase of gravitational coalescence requires precise predictions since the signal stays in the band for a long time. The method of scattering amplitudes has risen to a prominent role in this endeavor, with  LeCosPA's faculty member Prof. Chia-Hsien Shen being one of the pioneers.

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Concretely, the classical dynamics of binary systems can be encoded in scattering amplitudes of massive particles interacting through gravitons. Moderns amplitudes methods (double copy, generalized unitarity, multi-loop integration methods, etc.) can then be used to obtain a precise modeling of GW sources. The results are in a form that can be used by the LIGO theorists to construct waveform models.

An important goal of future GW science is the search for new physics beyond the standard models of particle physics and gravity. The aforementioned precision calculations in Einstein gravity provide the backbone for such an endeavor. For instance, any deviation from the spin multipole moments of rotating black holes could be a sign of modified gravity or the presence of new light degrees of freedom.

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The latter are generated by superradiance around spinning black holes forming so-called gravitational atoms. Prof. Baumann and collaborators studied what would happen when such atoms are part of binary systems. The found that the gravitational perturbation due to the companion can induce resonant transition between the different states of the cloud, which in turn affects the dynamics of the binary and hence the emitted gravitational waves. Observing these characteristic imprints in the GW signals would be an important test for theories that predict ultralight bosonic particles. While current GW observations aren't yet sensitive enough to observe the effect, it will become an important target of future experiments.