Searching for cosmological stochastic backgrounds by notching out resolvable compact binary foregrounds with next-generation gravitational-wave detectors

Stochastic gravitational-wave backgrounds can be of either cosmological or astrophysical origin. The detection of an astrophysical stochastic gravitational-wave background with ground-based interferometers is expected in the near future. Perhaps even more excitingly, the detection of stochastic backgrounds of cosmological origin by future ground-based interferometers could reveal invaluable information about the early Universe. From this perspective, the astrophysical background is a {\it foreground} that can prevent the extraction of this information from the data. In this paper, we revisit a time-frequency domain notching procedure previously proposed to remove the astrophysical foreground in the context of next-generation ground-based detectors, but we consider the more realistic scenario where we remove individually detectable signals by taking into account the uncertainty in the estimation of their parameters. We find that time-frequency domain masks can still efficiently remove the astrophysical foreground and suppress it to about $5\%$ of its original level. Further removal of the foreground formed by unresolvable events (in particular, unresolvable binary neutron stars), which is about $10$ times larger than the residual foreground from realistic notching, would require detector sensitivity improvements. Therefore, the main limitation in the search for a cosmological background is the unresolvable foreground itself, and not the residual of the notching procedure.