Multimessenger consistency relations bridging gravitational wave and large scale structure observations
Antonio Enea Romano
TL;DR
This work develops parametrization-independent consistency relations for Horndeski theories using the EFT of dark energy, linking observable quantities such as the effective gravitational constant $G_{ m eff}$, the slip parameter $\bar{\eta}$, the GW-EMW luminosity-distance ratio $d_L^{GW}/d_L^{EM}$, the GW speed $v_{GW}$, and the scalar sound speed $c_s$. By analyzing limiting cases (NSL, NB, CB, PLB) and a general Horndeski multi-probe condition, the authors provide compact analytical relations and a general non-compact condition that connect LSS and GW observables without fixing parameterizations. They map DESI-like LSS constraints on $G^{\Psi}_{\rm eff}$ and $G^{\Psi+\Phi}_{\rm eff}$ to predictions for $d_L^{GW}/d_L^{EM}$ under luminal propagation and show consistency with no-brading, illustrating the potential of joint GW–LSS analyses to test gravity in a model-independent way. A generalized phenomenological CR is also proposed, enabling data-driven tests across a broad Horndeski parameter space, with implications for future multimessenger cosmology and possible extensions to gravitational lensing. Overall, the paper provides a principled framework to infer or bound the effective gravitational coupling with multimessenger observations, independent of large-scale structure parametrizations.
Abstract
We show that for Horndeski theories it is possible to derive mathematically compact consistency relations (CR) between physically observable quantities, valid for different classes of theories defined by the behavior of the brading function $α_B$, independent of all other property functions. The CRs establish a parametrization independent direct relation between the effective gravitational constant, the slip parameter, the gravitational and electromagnetic waves (EMW) luminosity distances, the speed of gravitational waves (GW) and the sound speed. The no-brading CR is also satisfied by general relativity (GR), and allows to estimate the gravitational coupling from GWs observations, independently from large scale structure (LSS) observations. A general, less mathematically compact, consistency condition is also derived, valid for any form of the function $α_B$ and the other property functions. We apply the CRs to map the large scale structure observational constraints on the effective gravitational constant and the slip parameter to GW-EMW distance ratio constraints, showing that LSS and GWs give independent constraints consistent with no-brading. Beside allowing to perform parametrization and model independent tests of the consistency between different constraints on modified gravity, the CRs allow to probe the value of the effective gravitational constant with multimessenger observations, independently from LSS observations.