Cosmography with gravitational waves I: Taylor expansion in the low-redshift regime

We evaluate the capability of current and next-generation gravitational-wave detectors, including Advanced LIGO, the Einstein Telescope, and DECIGO, to probe cosmographic parameters using electromagnetically bright standard sirens. Adopting a third-order Taylor expansion, we examine the constraints primarily as a function of the number of detections and, in a complementary analysis, across correlated SNR--redshift regimes. Advanced LIGO can provide a distance-ladder-independent measurement of $H_0$ at the percent level. As the catalogue size increases, the Einstein Telescope reaches subpercent precision on $H_0$ and measures $q_0$ at the tens-of-percent level. DECIGO extends this sensitivity to $j_0$, achieving precision at the few-tens-of-percent level.