Abstract
We use gravitational wave (GW) standard sirens, in addition to Type Ia supernovae (SNIa) and baryon acoustic oscillation (BAO) mock data, to forecast constraints on the electromagnetic and gravitational distance duality relations (DDR) . We make use of a parameterised approach based on a specific DDR violation model, along with a machine learning reconstruction method based on the Genetic Algorithms. We find that GW provide an alternative to the use of BAO data to constrain violations of the DDR, reaching 3% constraints on the violation parameter we consider when combined with SNIa, which is only improved by a factor of ≈1.4 if one instead considers the combination of BAO and SNIa. We also investigate the possibility that a neglected modification of gravity might lead to a false detection of DDR violations, even when screening mechanisms are active. We find that such a false detection can be extremely significant, up to ≈10σ for very extreme modified gravity scenarios, while this reduces to ≈4σ in a more realistic case. False detections can also provide a smoking gun for the modified gravity mechanism at play, as a result of the tension introduced between the SNIa+GW and SNIa+BAO combinations.