Gravitational-wave confusion background from cosmological compact binaries: Implications for future terrestrial detectors

Increasing the sensitivity of a gravitational-wave (GW) detector improves our ability to measure the characteristics of detected sources. It also increases the number of weak signals that contribute to the data. Because GW detectors have nearly all-sky sensitivity, they can be subject to a confusion limit: Many sources which cannot be distinguished may be measured simultaneously, defining a stochastic noise floor to the sensitivity. For GW detectors operating at present and for their planned upgrades, the projected event rate is sufficiently low that we are far from the confusion-limited regime. However, some detectors currently under discussion may have large enough reach to binary inspiral that they enter the confusion-limited regime. In this paper, we examine the binary inspiral confusion limit for terrestrial detectors. We consider a broad range of inspiral rates in the literature, several planned advanced gravitational-wave detectors, and the highly advanced "Einstein telescope" design. Though most advanced detectors will not be impacted by this limit, the Einstein telescope with a very low-frequency "seismic wall" may be subject to confusion noise. At a minimum, careful data analysis will be require to separate signals which will appear confused. This result should be borne in mind when designing highly advanced future instruments.