Testing the consistency of gravitational waves and large scale structure constraints on dark energy

Gravitational wave (GW) astronomy has opened a new window on the Universe, allowing to obtain constraints on dark energy and gravity independent from other electromagnetic waves observations, such as large scale structure (LSS). For the purpose of investigating the consistency between different observations the effective field theory (EFT) of dark energy is a useful tool, allowing to derive model and parametrization independent consistency relations (CR) between the effective gravitational constant, the slip parameter, the gravitational and electromagnetic luminosity (EM) distance, and the speed of GWs. We test the constant brading and no-slip CRs, by comparing for the first time the constraints on the effective gravitational coupling obtained from LSS observations with those from GW events with and without electromagnetic counterparts, confirming the validity of the CRs at the current level of experimental uncertainty. The event GW170817 and its electromagnetic counterpart provides a constraint of the effective gravitational constant with an accuracy comparable with LSS constraints, while the analysis of GW events without electromagnetic counterpart are consistent, but do not have a constraining power comparable to LSS observations. Beside allowing to test the consistency between independent observations, the CRs can be used to estimate the effective gravitational coupling with GWs at high redshift, where other observations are not available.