Detecting cosmological gravitational wave background after removal of compact binary coalescences in future gravitational wave detectors

The improved sensitivity of third generation gravitational wave detectors opens the possibility of detecting the primordial cosmological stochastic gravitational wave background (SGWB). Detection of the cosmological SGWB is facing a novel challenge: it will likely be masked by the foreground generated by a large number of coalescences of compact binary systems consisting of black holes and/or neutron stars. In this paper, we investigate the possibility of reducing this foreground by removing (notching) the individually resolved compact binary signals in time-frequency space. We establish that such an approach could be used to reach the SGWB sensitivity floor defined by the unresolved part of the compact binaries foreground, which we find to be between ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{GW}}\ensuremath{\sim}(9.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}--8.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11})$ for a frequency independent energy density spectrum and depending on the rate of coalescing binary neutron star systems. Since third-generation gravitational wave detectors will not be able to resolve all compact binaries, the unresolvable component of the compact binaries foreground may limit the SGWB searches with these detectors.