Gravitational wave source counts at high redshift and in models with extra dimensions

Abstract

Gravitational wave (GW) source counts have been recently shown to be able to test how gravitational radiation propagates with the distance from the source. Here, we extend this formalism to cosmological scales, i.e. the high redshift regime, and we discuss the complications of applying this methodology to high redshift sources. We also allow for models with compactified extra dimensions like in the Kaluza-Klein model. Furthermore, we also consider the case of intermediate redshifts, i.e. $0<z\lesssim1$, where we show it is possible to find an analytical approximation for the source counts $\frac{dN}{d(S/N)}$. This can be done in terms of cosmological parameters, such as the matter density $Ω_{m,0}$ of the cosmological constant model or the cosmographic parameters for a general dark energy model. Our analysis is as general as possible, but it depends on two important factors: a source model for the black hole binary mergers and the GW source to galaxy bias. This methodology also allows us to obtain the higher order corrections of the source counts in terms of the signal-to-noise $S/N$. We then forecast the sensitivity of future observations in constraining GW physics but also the underlying cosmology by simulating sources distributed over a finite range of signal-to-noise with a number of sources ranging from 10 to 500 sources as expected from future detectors. We find that with 500 events it will be possible to provide constraints on the matter density parameter at present $Ω_{m,0}$ on the order of a few percent and with the precision growing fast with the number of events. In the case of extra dimensions we find that depending on the degeneracies of the model, with 500 events it may be possible to provide stringent limits on the existence of the extra dimensions if the aforementioned degeneracies can be broken.