Cosmology

Redshift

Einstein Telescope

Gravitational wave

Quantum

Quantum gravity

Physics

Luminosity

Cosmic microwave background

Gravitation

Luminosity distance

Mathematical physics

Galaxy

Astrophysics

Quantum mechanics

Anisotropy

f(R) gravity

General relativity

Lambda

Classical mechanics

Dark energy

Equation of state

Physical review. D/Physical review. D.

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.

Gravitational-wave luminosity distance in modified gravity theories