Standard sirens with a running Planck mass

We consider the effect of a time-varying Planck mass on the propagation of gravitational waves (GWs). A running Planck mass arises naturally in several modified-gravity theories, and here we focus on those that carry an additional dark energy field responsible for the late-time accelerated expansion of the Universe, yet---like general relativity (GR)---propagate only two GW polarizations, both traveling at the speed of light. Because a time-varying Planck mass affects the amplitude of the GWs and therefore the inferred distance to the source, standard siren measurements of ${H}_{0}$ are degenerate with the parameter ${c}_{M}$ characterizing the time-varying Planck mass, where ${c}_{M}=0$ corresponds to GR with a constant Planck mass. The effect of nonzero ${c}_{M}$ will have a noticeable impact on GWs emitted by binary neutron stars (BNSs) at the sensitivities and distances observable by ground-based GW detectors such as Advanced LIGO and $\mathrm{A}+$, implying that standard siren measurements can provide joint constraints on ${H}_{0}$ and ${c}_{M}$. Assuming a $\mathrm{\ensuremath{\Lambda}}$ cold dark matter evolution of the Universe and taking Planck's measurement of ${H}_{0}$ as a prior, we find that GW170817 constrains ${c}_{M}=\ensuremath{-}{9}_{\ensuremath{-}28}^{+21}$ (68.3% credibility). We also discuss forecasts, finding that if we assume ${H}_{0}$ is known independently (e.g., from the cosmic microwave background), then 100 BNS events detected by Advanced LIGO can constrain ${c}_{M}$ to within $\ifmmode\pm\else\textpm\fi{}0.9$. This is comparable to the current best constraints from cosmology. Similarly, for 100 LIGO $\mathrm{A}+$ BNS detections, it is possible to constrain ${c}_{M}$ to $\ifmmode\pm\else\textpm\fi{}0.5$. When analyzing joint ${H}_{0}$ and ${c}_{M}$ constraints we find that $\ensuremath{\sim}400$ LIGO $\mathrm{A}+$ events are needed to constrain ${H}_{0}$ to 1% accuracy. Finally, we discuss the possibility of a nonzero value of ${c}_{M}$ biasing standard siren ${H}_{0}$ measurements from 100 LIGO $\mathrm{A}+$ detections, and find that ${c}_{M}=+1.35$ could bias ${H}_{0}$ by $3\ensuremath{\sigma}$ to $4\ensuremath{\sigma}$ too low if we incorrectly assume ${c}_{M}=0$.