Listening to dark sirens from gravitational waves : Combined effects of fifth force, ultralight particle radiation, and eccentricity

We analyse the orbital period decay in compact binary systems influenced by a fifth force and ultralight particle radiation, considering a general eccentric Keplerian orbit. The analysis provides constraints on the axion decay constant when orbital period decay involves axionic fifth force and axion radiation. The bound on axion coupling improves by an order of magnitude for high eccentricity binaries like the Hulse–Taylor binary. These bounds become stronger when considering both axion mediation and radiation. We also derive constraints on the strengths of the fifth force and radiation from GW170817 by measuring the Chirp mass, which depends on initial eccentricity. The coalescence time increases with higher initial eccentricity compared to the gravity-only scenario, highlighting the importance of accurately selecting initial eccentricity for setting bounds on fifth force searches in precision gravitational wave detection. Additionally, we provide model-independent estimates for dark matter capture by a binary system. The derived constraints can be further strengthened with the use of second and third generation gravitational wave detectors.