Will cosmic gravitational wave sirens determine the Hubble constant?

Incorrect assumptions about the background expansion history of the Universe can induce significant biases when estimating the Hubble constant $H_0$ and other key cosmological parameters from cosmic ($z\gtrsim 0.1$) gravitational wave standard sirens, even with electromagnetic counterpart redshifts. Future gravitational wave experiments such as the Einstein Telescope can provide us with a compilation of gravitational wave sirens that can be used to determine these cosmological parameters with very high precision. In such a future, the statistical precision can reach to the level of 1% uncertainty on $H_0$. However, such datasets would include a large number of cosmic gravitational wave sirens, and not only sources at very low redshifts of $z\lesssim 0.1$. We show that wrong assumptions about the background expansion history of the Universe (e.g. form of dark energy) can introduce substantial bias in estimation of the Hubble constant and the other key parameters. Such biases would occur in non-$\Lambda$CDM cosmologies that can be degenerate with the standard $\Lambda$CDM model. To avoid model-dependent biases, statistical techniques that are appropriately agnostic about model assumptions need to be employed.