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 non-zero 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 A+ , implying that standard siren measurements can provide joint constraints on H _ { 0 } and c _ { M } .
Assuming a \Lambda CDM evolution of the universe and taking Planck ’ s measurement of H _ { 0 } as a prior , we find that GW170817 constrains c _ { M } = -9 ^ { +21 } _ { -28 } ( 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 \pm 0.9 .
This is comparable to the current best constraints from cosmology .
Similarly , for 100 LIGO A+ BNS detections , it is possible to constrain c _ { M } to \pm 0.5 .
When analyzing joint H _ { 0 } and c _ { M } constraints we find that \sim 400 LIGO 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 A+ detections , and find that c _ { M } = +1.35 could bias H _ { 0 } by 3–4 \sigma too low if we incorrectly assume c _ { M } = 0 .