The gravitational-wave luminosity distance in modified gravity theories
  In modified gravity the propagation of gravitational waves (GWs) is in
general different from that in general relativity. As a result, the luminosity
distance for GWs can differ from that for electromagnetic signals, and is
affected both by the dark energy equation of state $w_{\rm DE}(z)$ and by a
function $\delta(z)$ describing modified propagation. We show that the effect
of modified propagation in general dominates over the effect of the dark energy
equation of state, making it easier to distinguish a modified gravity model
from $\Lambda$CDM. We illustrate this using a nonlocal modification of gravity,
that has been shown to fit remarkably well CMB, SNe, BAO and structure
formation data, and we discuss the prospects for distinguishing nonlocal
gravity from $\Lambda$CDM with the Einstein Telescope. We find that, depending
on the exact sensitivity, a few tens of standard sirens with measured redshift
at $z\sim 0.4$, or a few hundreds at $1 < z < 2$, could suffice.
