  The study of current gravitational waves catalogues provide an interesting
model independent way to understand further the nature of dark energy. Taking
advantage of them, in this work we present an update of the constraints related
to dynamical dark energy parameterisations using recent Gravitational-Wave
Transient catalogues (GWTC1 and GWTC-2). Also, we present a new treatment for
GW to establish the relation between the standard luminosity distance and the
siren distance. According to our Bayesian results developed with our join
SNeIa+CC+GW database, the $\Lambda$CDM model shows a preference against all the
dark energy parameterisations considered here. Moreover, with the current GW
transient database the GR standard luminosity and siren distances ratio shows a
strong preference against the modified gravity $\delta$-models considered here.
