Constraining the Einstein-dilaton-Gauss-Bonnet theory with higher harmonics and the merger-ringdown contribution using GWTC-3

In this paper, we revisit the problem of using gravitational wave data to test the Einstein-dilation-Gauss-Bonnet theory by using nine selected gravitational wave events from the third Gravitational-Wave Transient Catalog. Compared with existing work, we take into account the higher harmonics more properly and we also study the contribution of the merger-ringdown data. Using the inspiral data alone, we find that the best result is from GW200115, giving $\sqrt{|\ensuremath{\alpha}|}<1.1\text{ }\text{ }\mathrm{km}$, which is about 17% tighter than the previous best result. Several combinations of the selected events give $\sqrt{|\ensuremath{\alpha}|}\ensuremath{\le}1.0\text{ }\text{ }\mathrm{km}$. The result is further improved when the merger-ringdown data are also included, using two phenomenological schemes, giving $\sqrt{|\ensuremath{\alpha}|}<0.87\text{ }\text{ }\mathrm{km}$ for GW200115 in the best case scenario. We also notice the possible existence of a simple unexpected relation among the constraints from different events, and it is important to have more large mass ratio events that can help clarify if there is indeed such a trend.