Consistency between cosmological and standard siren observations in evolving dark energy
A scalar field non-minimally coupled to gravity can be the driver of cosmic acceleration. Such a non-minimal coupling (NMC) can produce a non-zero gravitational-wave (GW) friction function $\alpha_M(z)$, which modifies the luminosity distance inferred from GW sources relative to its electromagnetic counterpart. We use a particular NMC scalar-tensor model, that explains time-varying dark energy in good alignment with DESI, to predict $\alpha_M(z)$ and the expected GW/EM luminosity-distance ratio $D_L^{\rm GW}/D_L^{\rm EM}$, and map it onto two common parametrizations---the $c_M$ and the $(\Xi_0,n)$ models. We find $c_M = -0.5\pm 0.2$ and $\Xi_0 = 0.88\pm 0.05$, $n=3.2\pm 0.3$, both consistent with GWTC-5 constraints at the $\lesssim 1\sigma$ level. This consistency is mostly driven by current large uncertainties in GW data, which lead to measurements consistent with both $\Lambda$CDM and the NMC model. By contrast, the dark energy constraints derived from analyzing cosmological data, under the common parametric scalar-tensor model using $\alpha_M(z)=c_M\Omega_\Lambda(z)/\Omega_{\Lambda 0}$ and the CPL parametrized equation of state $w_0w_a$, are in $2.2\sigma$ ($3.6\sigma$) tension with the NMC predictions for the $c_M$ ($w_0w_a$) parameter. We confirm that, in order to avoid cosmological instabilities, this parametrized model imposes strong implicit priors that are incompatible with physically-motivated scalar-tensor models when dark energy is dynamical.