Gravitational waves from binary black holes in a self-interacting scalar dark matter cloud

We investigate the imprints of accretion and dynamical friction on the gravitational-wave signals emitted by binary black holes embedded in a scalar dark matter cloud. As a key feature in this work, we focus on scalar fields with a repulsive self-interaction that balances against the self-gravity of the cloud. To a first approximation, the phase of the gravitational-wave signal receives extra correction terms at -3PN, -4PN, and -5.5PN orders, relative to the prediction of vacuum general relativity, due to cloud gravity, accretion and dynamical friction. Future observations by LISA and DECIGO have the potential to detect these effects for a large range of scalar masses mDM and self-interaction couplings lambda 4. This would correspond to scenarios with dark matter clouds smaller than 0.1 pc, which would be difficult to detect by other probes.